To see the other types of publications on this topic, follow the link: Lyapunov stability theory.
Dissertations / Theses on the topic 'Lyapunov stability theory'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Lyapunov stability theory.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Grünvogel, Stefan Michael. "Lyapunov spectrum and control sets." Augsburg [Germany] : Wissner-Verlag, 2000. http://catalog.hathitrust.org/api/volumes/oclc/45796984.html.
Full text
2
Thomas, Neil B. "The analysis and control of nonlinear systems using Lyapunov stability theory." Thesis, This resource online, 1996. http://scholar.lib.vt.edu/theses/available/etd-08292008-063459/.
Full text
3
Ahmadi, Amir Ali. "Non-monotonic Lyapunov functions for stability of nonlinear and switched systems : theory and computation." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/44206.
Full textAbstract:
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 87-90).
Lyapunov's direct method, which is based on the existence of a scalar function of the state that decreases monotonically along trajectories, still serves as the primary tool for establishing stability of nonlinear systems. Since the main challenge in stability analysis based on Lyapunov theory is always to nd a suitable Lyapunov function, weakening the requirements of the Lyapunov function is of great interest. In this thesis, we relax the monotonicity requirement of Lyapunov's theorem to enlarge the class of functions that can provide certicates of stability. Both the discrete time case and the continuous time case are covered. Throughout the thesis, special attention is given to techniques from convex optimization that allow for computationally tractable ways of searching for Lyapunov functions. Our theoretical contributions are therefore amenable to convex programming formulations. In the discrete time case, we propose two new sucient conditions for global asymptotic stability that allow the Lyapunov functions to increase locally, but guarantee an average decrease every few steps. Our first condition is nonconvex, but allows an intuitive interpretation. The second condition, which includes the first one as a special case, is convex and can be cast as a semidenite program. We show that when non-monotonic Lyapunov functions exist, one can construct a more complicated function that decreases monotonically. We demonstrate the strength of our methodology over standard Lyapunov theory through examples from three different classes of dynamical systems. First, we consider polynomial dynamics where we utilize techniques from sum-of-squares programming. Second, analysis of piecewise ane systems is performed. Here, connections to the method of piecewise quadratic Lyapunov functions are made.
(cont.) Finally, we examine systems with arbitrary switching between a finite set of matrices. It will be shown that tighter bounds on the joint spectral radius can be obtained using our technique. In continuous time, we present conditions invoking higher derivatives of Lyapunov functions that allow the Lyapunov function to increase but bound the rate at which the increase can happen. Here, we build on previous work by Butz that provides a nonconvex sucient condition for asymptotic stability using the first three derivatives of Lyapunov functions. We give a convex condition for asymptotic stability that includes the condition by Butz as a special case. Once again, we draw the connection to standard Lyapunov functions. An example of a polynomial vector field is given to show the potential advantages of using higher order derivatives over standard Lyapunov theory. We also discuss a theorem by Yorke that imposes minor conditions on the first and second derivatives to reject existence of periodic orbits, limit cycles, or chaotic attractors. We give some simple convex conditions that imply the requirement by Yorke and we compare them with those given in another earlier work. Before presenting our main contributions, we review some aspects of convex programming with more emphasis on semidenite programming. We explain in detail how the method of sum of squares decomposition can be used to efficiently search for polynomial Lyapunov functions.
by Amir Ali Ahmadi.
S.M.
4
Shifman, Jeffrey Joseph. "The control of flexible robots." Thesis, University of Cambridge, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.385838.
Full text
5
Herzog, David Paul. "Geometry's Fundamental Role in the Stability of Stochastic Differential Equations." Diss., The University of Arizona, 2011. http://hdl.handle.net/10150/145150.
Full textAbstract:
We study dynamical systems in the complex plane under the effect of constant noise. We show for a wide class of polynomial equations that the ergodic property is valid in the associated stochastic perturbation if and only if the noise added is in the direction transversal to all unstable trajectories of the deterministic system. This has the interpretation that noise in the "right" direction prevents the process from being unstable: a fundamental, but not well-understood, geometric principle which seems to underlie many other similar equations. The result is proven by using Lyapunov functions and geometric control theory.
6
Dierks, Travis. "Formation control of mobile robots and unmanned aerial vehicles." Diss., Rolla, Mo. : Missouri University of Science and Technology, 2009. http://scholarsmine.mst.edu/thesis/pdf/Dierks_09007dcc806d7f16.pdf.
Full textAbstract:
Thesis (Ph. D.)--Missouri University of Science and Technology, 2009.Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed January 13, 2009) Includes bibliographical references.
7
Li, Yunyan. "Global finite-time observers for a class of nonlinear systems." Thesis, University of Pretoria, 2013. http://hdl.handle.net/2263/40825.
Full textAbstract:
The contributions of this thesis lie in the area of global finite-time observer design for a class of
nonlinear systems with bounded rational and mixed rational powers imposed on the incremental rate
of the nonlinear terms whose solutions exist and are unique for all positive time. In the thesis, two
different kinds of nonlinear global finite-time observers are designed by employing of finite-time
theory and homogeneity properties with different methods. The global finite-time stability of both
proposed observers is derived on the basis of Lyapunov theory.
For a class of nonlinear systems with rational and mixed rational powers imposed on the nonlinearities,
the first global finite-time observers are designed, where the global finite-time stability of the
observation systems is achieved from two parts by combining asymptotic stability and local finitetime
stability. The proposed observers can only be designed for the class of nonlinear systems with
dimensions greater than 3. The observers have a dynamic high gain and two homogenous terms, one
homogeneous of degree greater than 1 and the other of degree less than 1. In order to prove the global
finite-time stability of the proposed results, two homogeneous Lyapunov functions are provided, corresponding
with the two homogeneous items. One is homogeneous of degree greater than 1, which
makes the observation error systems converging into a spherical area around the origin, and the other
is of degree less than 1, which ensures local finite-time stability.
The second global finite-time observers are also proposed based on the high-gain technique, which
does not place any limitation on the dimension of the nonlinear systems. Compared with the first
global finite-time observers, the newly designed observers have only one homogeneous term and a
new gain update law where two new terms are introduced to dominate some terms in the nonlinearities
and ensure global finite-time stability as well. The global finite-time stability is obtained directly
based on a sufficient condition of finite-time stability and only one Lyapunov function is employed in
the proof.
The validity of the two kinds of global finite-time observers that have been designed is illustrated through some simulation results. Both of them can make the observation error systems converge to
the origin in finite-time. The parameters, initial conditions as well as the high gain do have some
impact on the convergence time, where the high gain plays a stronger role. The bigger the high gain
is, the shorter the time it needs to converge. In order to show the performance of the two kinds of
observers more clearly, two examples are provided and some comparisons are made between them.
Through these, it can be seen that under the same parameters and initial conditions, although the
amplitude of the observation error curve is slightly greater, the global finite-time observers with a
new gain update law can make the observation error systems converge much more quickly than the
global finite-time observers with two homogeneous terms. In the simulation results, one can see that,
as a common drawback of high gain observers, they are noise-sensitive. Finding methods to improve
their robustness and adaptiveness will be quite interesting, useful and challenging.Thesis (PhD)--University of Pretoria, 2013.
gm2014
Electrical, Electronic and Computer Engineering
unrestricted
8
Hui, Qing. "Nonlinear dynamical systems and control for large-scale, hybrid, and network systems." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24635.
Full textAbstract:
Thesis (Ph.D.)--Aerospace Engineering, Georgia Institute of Technology, 2009.Committee Chair: Haddad, Wassim; Committee Member: Feron, Eric; Committee Member: JVR, Prasad; Committee Member: Taylor, David; Committee Member: Tsiotras, Panagiotis
9
Sousa, Júnior Celso de. "Análise de estabilidade de Lyapunov de algoritmos adaptativos com contribuições ao estudo do critério de módulo constante." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/260851.
Full textAbstract:
Orientadores: João Marcos Travassos Romano, Romis Ribeiro de Faissol AttuxTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação
Made available in DSpace on 2018-08-19T00:40:42Z (GMT). No. of bitstreams: 1 SousaJunior_Celsode_D.pdf: 2582555 bytes, checksum: 4c20b08e97e42d51ea143f7651c91af4 (MD5) Previous issue date: 2011
Resumo: O problema de equalização adaptativa se vincula à busca por soluções iterativas que permitam reduzir ou eliminar os efeitos nocivos do canal de comunicação sobre um sinal transmitido de interesse. Uma vez que os sistemas adaptativos se baseiam em algoritmos capazes de ajustar os parâmetros de um filtro, pode-se considerar o conjunto equalizador / algoritmo adaptativo como um sistema dinâmico, o que termina por relacionar a possibilidade de obter uma solução satisfatória à noção de convergência. A análise de convergência de algoritmos de equalização adaptativa se desenvolveu, tipicamente, considerando algumas hipóteses para viabilizar o tratamento matemático, mas nem sempre tais hipóteses são estritamente válidas. Um exemplo clássico nesse sentido é o uso da teoria da independência. Neste trabalho, buscamos uma abordagem distinta do estudo das condições de estabilidade de algoritmos de equalização clássica baseada na teoria de Lyapunov. Essa teoria é geralmente utilizada no estudo de sistemas não-lineares, e apresenta um amplo histórico de resultados sólidos na área de controle adaptativo. Isso motiva o uso no campo de processamento de sinais. A primeira contribuição deste trabalho consiste em determinar, por meio da teoria de Lyapunov, a faixa de valores de passo de adaptação que garantem estabilidade do sistema de equalização para algoritmos baseados no critério deWiener e para o algoritmo do módulo constante. A partir dos resultados para estabilidade, investigar-se-á também a região de convergência para os pesos do algoritmo LMS, o que trará uma produtiva relação com a idéia de misadjustment. Como segunda linha de contribuição, será apresentada uma análise de um limitante inferior para o custo atingível e uma proposta de inicialização capaz de aumentar a probabilidade de convergência para o melhor ótimo gerado pelo critério para o algoritmo do módulo constante. Essa estratégia se baseia numa formulação do critério não-supervisionado de filtragem linear em termos da aplicação do critério de Wiener a uma estrutura polinomial. Os resultados obtidos revelam que a idéia é capaz de levar a um desempenho melhor que os do clássico método center spike e de uma estratégia de inicialização aleatória
Abstract: The problem of adaptive equalization is related to the search for iterative solutions that allow the reduction or the elimination of the noxious effects of a communication channel on a transmitted signal of interest. Since adaptive systems are based on algorithms capable of adjusting the parameters of a filter, the combination between equalizer and learning algorithm can be considered to form a dynamical system, which relates the possibility of obtaining a satisfactory solution to the convergence issue. The analysis of the convergence of adaptive equalization algorithms was developed, typically, considering certain simplifying hypotheses that, however, are not always strictly valid. A classical example that illustrates this assertion is the use of the so-called independence theory. In this work, it has been investigated a distinct approach to the study of stability conditions of classical methods based on Lyapunov theory. This theory is generally employed in the study of nonlinear systems, and presents a significant framework of sound results in the field of adaptive control, which motivates its use in the context of signal processing. The first contribution of this work consists of determining, by means of Lyapunov theory, the range of step-size values that ensure stability of the equalization system for algorithms based on the Wiener criterion and for the constant modulus algorithm. Using the obtained stability results, the convergence region for the parameters estimated via LMS is also investigated, which establishes an interesting connection with the notion of misadjustment. In a second line of study, we present an analysis of the lower bound for the attainable CM cost and an initialization heuristic capable of increasing the probability of convergence to the best optimum engendered by the constant modulus criterion. This strategy is based on a formulation of the unsupervised linear filtering criterion in terms of the application of the Wiener criterion to a polynomial structure. The obtained results reveal that the proposal is able to effectively lead to a performance level that is better than that achieved using the classical center spike method and a random approach
Doutorado
Telecomunicações e Telemática
Doutor em Engenharia Elétrica
10
Tognetti, Tais Calliero. "Controle de sistemas dinamicos : estabilidade absoluta, saturação e bilinearidade." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261053.
Full textAbstract:
Orientador: Pedro Luis Dias PeresTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
Made available in DSpace on 2018-08-14T19:01:41Z (GMT). No. of bitstreams: 1 Tognetti_TaisCalliero_D.pdf: 1438301 bytes, checksum: 87c3292b4b408bcddec959f4f9e45317 (MD5) Previous issue date: 2009
Resumo: Esta tese apresenta contribuições para a solução de problemas de análise de estabilidade e síntese de controladores por realimentação de estados de sistemas dinâmicos que possuem elementos não-lineares, por meio de condições na forma de desigualdades matriciais lineares e funções de Lyapunov. Para sistemas chaveados sujeitos a saturação nos atuadores, são fornecidas condições convexas para o cálculo de ganhos chaveados e robustos. A saturação é modelada como uma não-linearidade de setor e uma estimativa do domínio de estabilidade é determinada. Para sistemas lineares com incertezas politópicas e não-linearidades pertencentes a setores, são fornecidas condições convexas de dimensão finita para construir funções de Lur'e com dependência polinomial homogênea nos parâmetros. Se satisfeitas, as condições garantem a estabilidade para todo o domínio de incertezas e para todas as não-linearidades pertencentes ao setor e permitem o cômputo de controladores estabilizantes robustos por realimentação linear e não-linear. Para sistemas bilineares instáveis, contínuos e discretos no tempo, é proposto um procedimento para calcular um ganho estabilizante de controle por realimentação de estados. O método baseia-se na solução alternada de dois problemas de otimização convexa descritos por desigualdades matriciais lineares, fornecendo uma estimativa do domínio de estabilidade. Extensões para tratar controladores robustos e lineares variantes com parâmetros são também apresentadas.
Abstract: This thesis presents contributions to the solution of the problems of stability analysis and synthesis of state feedback controllers for dynamic systems with non-linear elements, by means of conditions based on linear matrix inequalities and Lyapunov functions. For switched systems subject to saturation in the actuators, convex conditions to design switched and robust controllers are presented. The saturation is modeled as a sector non-linearity and an estimate of the domain of stability is determined. For linear systems with polytopic uncertainties and sector non-linearities, convex conditions of finite dimension to build Lur'e functions with homogeneous polynomially parameter dependence are provided. If satisfied, the conditions guarantee the stability of the entire domain of uncertainty for all sector non-linearities, allowing the design of linear and non-linear robust state feedback stabilizing controllers. For continuous and discrete-time unstable bilinear systems, a procedure to design a state feedback stabilizing control gain is proposed. The method is based on the alternate solution of two convex optimization problems described by linear matrix inequalities, providing an estimate of the domain of stability. Extensions to handle robust and linear parameter varying controllers are also presented.
Doutorado
Automação
Doutor em Engenharia Elétrica
11
Oliveira, Heloisa Maria de 1982. "Redes de filas com escolha de servidor." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306090.
Full textAbstract:
Orientador: Marina VachkovskaiaTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
Made available in DSpace on 2018-08-21T12:11:37Z (GMT). No. of bitstreams: 1 Oliveira_HeloisaMariade_D.pdf: 1371327 bytes, checksum: 1913d92f9ff81812cfbf5b4fab73215d (MD5) Previous issue date: 2012
Resumo: Considere as redes de filas com N servidores e K tipos de trabalho. Suponha que os tipos de trabalho i chegam independentemente à rede de acordo com o processo de Poisson com taxa...Observação: O resumo, na íntegra, poderá ser visualizado no texto completo da tese digital
Abstract: Consider a queueing network with N servers and K types of jobs (or customer classes). The types of jobs i, i = 1; ¿ ;K, arrive at the system accordingly to independent Poisson process with rate...Note: The complete abstract is available with the full electronic document
Doutorado
Estatistica
Doutora em Estatística
12
Dando, Aaron John. "Robust adaptive control of rigid spacecraft attitude maneuvers." Thesis, Queensland University of Technology, 2008. https://eprints.qut.edu.au/16695/1/Aaron_John_Dando_Thesis.pdf.
Full textAbstract:
In this thesis novel feedback attitude control algorithms and attitude estimation algorithms are developed for a three-axis stabilised spacecraft attitude control system. The spacecraft models considered include a rigid-body spacecraft equipped with (i) external control torque devices, and (ii) a redundant reaction wheel configuration. The attitude sensor suite comprises a three-axis magnetometer and three-axis rate gyroscope assembly. The quaternion parameters (also called Euler symmetric parameters), which globally avoid singularities but are subject to a unity-norm constraint, are selected as the primary attitude coordinates. There are four novel contributions presented in this thesis. The first novel contribution is the development of a robust control strategy for spacecraft attitude tracking maneuvers, in the presence of dynamic model uncertainty in the spacecraft inertia matrix, actuator magnitude constraints, bounded persistent external disturbances, and state estimation error. The novel component of this algorithm is the incorporation of state estimation error into the stability analysis. The proposed control law contains a parameter which is dynamically adjusted to ensure global asymptotic stability of the overall closedloop system, in the presence of these specific system non-idealities. A stability proof is presented which is based on Lyapunov's direct method, in conjunction with Barbalat's lemma. The control design approach also ensures minimum angular path maneuvers, since the attitude quaternion parameters are not unique. The second novel contribution is the development of a robust direct adaptive control strategy for spacecraft attitude tracking maneuvers, in the presence of dynamic model uncertainty in the spacecraft inertia matrix. The novel aspect of this algorithm is the incorporation of a composite parameter update strategy, which ensures global exponential convergence of the closed-loop system. A stability proof is presented which is based on Lyapunov's direct method, in conjunction with Barbalat's lemma. The exponential convergence results provided by this control strategy require persistently exciting reference trajectory commands. The control design approach also ensures minimum angular path maneuvers. The third novel contribution is the development of an optimal control strategy for spacecraft attitude maneuvers, based on a rigid body spacecraft model including a redundant reaction wheel assembly. The novel component of this strategy is the proposal of a performance index which represents the total electrical energy consumed by the reaction wheel over the maneuver interval. Pontraygin's minimum principle is applied to formulate the necessary conditions for optimality, in which the control torques are subject to timevarying magnitude constraints. The presence of singular sub-arcs in the statespace and their associated singular controls are investigated using Kelley's necessary condition. The two-point boundary-value problem (TPBVP) is formulated using Pontrayagin's minimum principle. The fourth novel contribution is an attitude estimation algorithm which estimates the spacecraft attitude parameters and sensor bias parameters from three-axis magnetometer and three-axis rate gyroscope measurement data. The novel aspect of this algorithm is the assumption that the state filtering probability density function (PDF) is Gaussian distributed. This Gaussian PDF assumption is also applied to the magnetometer measurement model. Propagation of the filtering PDF between sensor measurements is performed using the Fokker-Planck equation, and Bayes theorem incorporates measurement update information. The use of direction cosine matrix elements as the attitude coordinates avoids any singularity issues associated with the measurement update and estimation error covariance representation.
13
Dando, Aaron John. "Robust adaptive control of rigid spacecraft attitude maneuvers." Queensland University of Technology, 2008. http://eprints.qut.edu.au/16695/.
Full textAbstract:
In this thesis novel feedback attitude control algorithms and attitude estimation algorithms are developed for a three-axis stabilised spacecraft attitude control system. The spacecraft models considered include a rigid-body spacecraft equipped with (i) external control torque devices, and (ii) a redundant reaction wheel configuration. The attitude sensor suite comprises a three-axis magnetometer and three-axis rate gyroscope assembly. The quaternion parameters (also called Euler symmetric parameters), which globally avoid singularities but are subject to a unity-norm constraint, are selected as the primary attitude coordinates. There are four novel contributions presented in this thesis. The first novel contribution is the development of a robust control strategy for spacecraft attitude tracking maneuvers, in the presence of dynamic model uncertainty in the spacecraft inertia matrix, actuator magnitude constraints, bounded persistent external disturbances, and state estimation error. The novel component of this algorithm is the incorporation of state estimation error into the stability analysis. The proposed control law contains a parameter which is dynamically adjusted to ensure global asymptotic stability of the overall closedloop system, in the presence of these specific system non-idealities. A stability proof is presented which is based on Lyapunov's direct method, in conjunction with Barbalat's lemma. The control design approach also ensures minimum angular path maneuvers, since the attitude quaternion parameters are not unique. The second novel contribution is the development of a robust direct adaptive control strategy for spacecraft attitude tracking maneuvers, in the presence of dynamic model uncertainty in the spacecraft inertia matrix. The novel aspect of this algorithm is the incorporation of a composite parameter update strategy, which ensures global exponential convergence of the closed-loop system. A stability proof is presented which is based on Lyapunov's direct method, in conjunction with Barbalat's lemma. The exponential convergence results provided by this control strategy require persistently exciting reference trajectory commands. The control design approach also ensures minimum angular path maneuvers. The third novel contribution is the development of an optimal control strategy for spacecraft attitude maneuvers, based on a rigid body spacecraft model including a redundant reaction wheel assembly. The novel component of this strategy is the proposal of a performance index which represents the total electrical energy consumed by the reaction wheel over the maneuver interval. Pontraygin's minimum principle is applied to formulate the necessary conditions for optimality, in which the control torques are subject to timevarying magnitude constraints. The presence of singular sub-arcs in the statespace and their associated singular controls are investigated using Kelley's necessary condition. The two-point boundary-value problem (TPBVP) is formulated using Pontrayagin's minimum principle. The fourth novel contribution is an attitude estimation algorithm which estimates the spacecraft attitude parameters and sensor bias parameters from three-axis magnetometer and three-axis rate gyroscope measurement data. The novel aspect of this algorithm is the assumption that the state filtering probability density function (PDF) is Gaussian distributed. This Gaussian PDF assumption is also applied to the magnetometer measurement model. Propagation of the filtering PDF between sensor measurements is performed using the Fokker-Planck equation, and Bayes theorem incorporates measurement update information. The use of direction cosine matrix elements as the attitude coordinates avoids any singularity issues associated with the measurement update and estimation error covariance representation.
14
Borges, Renato Alves. "Controle e filtragem de sistemas lineares variantes no tempo por meio de funções de Lyapunov dependentes de parametros." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261054.
Full textAbstract:
Orientador: Pedro Luis Dias PeresTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
Made available in DSpace on 2018-08-13T19:35:14Z (GMT). No. of bitstreams: 1 Borges_RenatoAlves_D.pdf: 1110575 bytes, checksum: 60707903258309c73eb16c6b81e8e7ba (MD5) Previous issue date: 2009
Resumo: A principal contribuição desta tese é a proposta de condições de sintese de filtros e controladores lineares, tanto robustos quanto dependentes de parametros, para sistemas discretos variantes no tempo.Os controladores, ou filtros, são obtidos solucionando problemas de otimização formulados em termos de desigualdades matriciais bililineares, por meio de um metodo que se baseia na alternancia de problemas convexos descritos por desigualdades matriciais lineares. Para obtenção das condiçoes de sintese foram utilizadas tanto funções de Lyapunov afins nos parâmetros quanto ametros, alem de variáveis multi-afins em diferentes instantes de tempo dos parâmetros, alem de variaveis extras introduzidas pelo lema de Finsler. Nesse contexto, sao tratados problemas de sintese com custo garantido H, assegurando robustez em relação a incertezas não estruturadas. Simulaçoes numéricas ilustram a eficiencia dos metodos propostos em termos de desempenho H quando comparados com outros metodos da literatura
Abstract: The main contribution of this dissertation is to propose conditions for linear filter and controller design, considering both robust and parameter dependent structures, for discrete time-varying systems. The controllers, or filters, are obtained through the solution of optimization problems, formulated in terms of bilinear matrix inequalities, using a method that alternates convex optimization problems described in terms of linear matrix inequalities. Both affine and multi-affine in different instants of time (path dependent)Lyapunov functions were usedto obtain the design conditions, as wellas extra variables introduced bythe Finsler's lemma.Design problems that take into account an H guaranteed cost were investigated, providing robustness with respect to unstructured uncertainties. Numerical simulations show the effciency of the proposed methods in terms of H performance when compared with other strategies from the literature
Doutorado
Automação
Doutor em Engenharia Elétrica
15
Moreira, Heber Rocha. "Realimentação de saida robusta a partir de controladores dependentes de parametros para sistemas lineares incertos discretos no tempo." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/259735.
Full textAbstract:
Orientadores: Pedro Luis Dias Peres, Ricardo Coração de Leão Fontoura de OliveiraDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
Made available in DSpace on 2018-08-14T06:55:42Z (GMT). No. of bitstreams: 1 Moreira_HeberRocha_M.pdf: 2003528 bytes, checksum: 9b091e7706d78e1298bd1d0603504e7f (MD5) Previous issue date: 2009
Resumo: Esta dissertação trata de um dos mais importantes problemas em aberto na teoria de controle, o projeto de controladores por realimentação estática de saída. A principal contribuição é propor um método para computar controladores robustos estáticos por realimentação de saída para sistemas lineares incertos discretos no tempo, usando um controlador por realimentação de estados como parâmetro de entrada do método. Além disso, os resultados são estendidos para tratar do projeto de controle H2 robusto por realimentação de saída. As condições de síntese são formuladas em termos de um procedimento convexo de otimização, baseado em um conjunto finito de desigualdades matriciais lineares. Exemplos numéricos são apresentados para ilustrar a eficiência dos metodos propostos quando comparados com outros métodos existentes na literatura.
Abstract: This thesis deals with one of the most important open problems in control theory, the design of static output feedback controllers. The main contribution is to propose a method to compute robust static output feedback controllers for uncertain linear discrete-time systems, using a state feedback controller as an input parameter for the method. Additionally, the results are extended to cope with H2 static output feedback control design. The synthesis conditions are formulated in terms of a convex optimization procedure, based on a finite set of linear matrix inequalities. Numerical examples are presented to illustrate the effectiveness of the proposed approach compared to other methods available in the literature.
Mestrado
Automação
Mestre em Engenharia Elétrica
16
Chu, Xing. "Commande distribuée, en poursuite, d'un système multi-robots non holonomes en formation." Thesis, Ecole centrale de Lille, 2017. http://www.theses.fr/2017ECLI0035/document.
Full textAbstract:
L’objectif principal de cette thèse est d’étudier le problème du contrôle de suivi distribué pour les systèmes de formation de multi-robots à contrainte non holonomique. Ce contrôle vise à entrainer une équipe de robots mobile de type monocycle pour former une configuration de formation désirée avec son centroïde se déplaçant avec une autre trajectoire de référence dynamique et pouvant être spécifié par le leader virtuel ou humain. Le problème du contrôle de suivi a été résolu au cours de cette thèse en développant divers contrôleurs distribués pratiques avec la considération d’un taux de convergence plus rapide, une précision de contrôle plus élevée, une robustesse plus forte, une estimation du temps de convergence explicite et indépendante et moins de coût de communication et de consommation d’énergie. Dans la première partie de la thèse nous étudions d’abord au niveau du chapitre 2 la stabilité à temps fini pour les systèmes de formation de multi-robots. Une nouvelle classe de contrôleur à temps fini est proposée dans le chapitre 3, également appelé contrôleur à temps fixe. Nous étudions les systèmes dynamiques de suivi de formation de multi-robots non holonomiques dans le chapitre 4. Dans la deuxième partie, nous étudions d'abord le mécanisme de communication et de contrôle déclenché par l'événement sur les systèmes de suivi de la formation de multi-robots non-holonomes au chapitre 5. De plus, afin de développer un schéma d'implémentation numérique, nous proposons une autre classe de contrôleurs périodiques déclenchés par un événement basé sur un observateur à temps fixe dans le chapitre 6The main aim of this thesis is to study the distributed tracking control problem for the multi-robot formation systems with nonholonomic constraint, of which the control objective it to drive a team of unicycle-type mobile robots to form one desired formation configuration with its centroid moving along with another dynamic reference trajectory, which can be specified by the virtual leader or human. We consider several problems in this point, ranging from finite-time stability andfixed-time stability, event-triggered communication and control mechanism, kinematics and dynamics, continuous-time systems and hybrid systems. The tracking control problem has been solved in this thesis via developing diverse practical distributed controller with the consideration of faster convergence rate, higher control accuracy, stronger robustness, explicit and independent convergence time estimate, less communication cost and energy consumption.In the first part of the thesis, we first study the finite-time stability for the multi-robot formation systems in Chapter 2. To improve the pior results, a novel class of finite-time controller is further proposed in Chapter 3, which is also called fixed-time controller. The dynamics of nonholonomic multi-robot formation systems is considered in Chapter 4. In the second part, we first investigate the event-triggered communication and control mechanism on the nonholonomic multi-robot formation tracking systems in Chapter 5. Moreover, in order to develop a digital implement scheme, we propose another class of periodic event-triggered controller based on fixed-time observer in Chapter 6
17
Stathas, Alexandros. "Numerical modeling of earthquake faults." Thesis, Ecole centrale de Nantes, 2021. http://www.theses.fr/2021ECDN0053.
Full textAbstract:
Lors d’un glissement sismique, l’énergie libérée par la décharge élastique des blocs de terre adjacente peut être séparée en trois parties principales : L’énergie qui est rayonnée à la surface de la terre (_ 5% du budget énergétique total), l’énergie de fracture pour la création de nouvelles surfaces de faille et enfin, l’énergie dissipée à l’intérieur d’une région de la faille, d’épaisseur finie, que l’on appelle le “fault gouge ". Cette région accumule la majorité du glissement sismique. Estimer correctement la largeur de fault gouge est d’une importance capitale pour calculer l’énergie dissipée pendant le séisme, le comportement frictionnel de la faille et les conditions de nucléation de la faille sous la forme d’un glissement sismique ou asismique.Dans cette thèse, approches différentes de régularisation ont été explorées pour l’estimation de la largeur de localisation de la zone de glissement principal de la faille pendant le glissement cosmique. Celles-ci comprennent l’application de la viscosité et des couplages multiphasiques dans le continuum classique de Cauchy, et l’introduction d’un continuum micromorphe de Cosserat du premier ordre. Tout d’abord, nous nous concentrons sur le rôle de la régularisation visqueuse dans le contexte des analyses dynamiques, en tant que méthode de régularisation de la localisation des déformations. Nous étudions le cas dynamique d’un continuum de Cauchy classique adoucissant à la déformation et durcissant à la vitesse de déformation. En appliquant l’analyse de stabilité de Lyapunov, nous montrons que l’introduction de la viscosité est incapable d’empêcher la localisation de la déformation sur un plan mathématique et la dépendance de du maillage des éléments finis.Nous effectuons des analyses non linéaires en utilisant le continuum de Cosserat dans le cas de grands déplacements par glissement sismique de fault gouge par rapport à sa largeur. Le continuum de Cosserat nous permet de rendre compte de l’énergie dissipée pendant un séisme et du rôle de la microstructure dans l’évolution de la friction de la faille. Nous nous concentrons sur l’influence de la vitesse de glissement sismique sur le mécanisme d’assidument frictionnel de la pressurisation thermique. Nous remarquons que l’influence des conditions aux limites dans la diffusion du fluide interstitiel à l’intérieur de fault gouge, conduit à une reprise du frottement après l’affaiblissement initial. De plus, un mode de localisation de déformation en mouvement est présent pendant le cisaillement de la couche, introduisant des oscillations dans la réponse du frottement. Ces oscillations augmentent le contenu spectral du séisme. L’introduction de la viscosité dans le mode ci-dessus, conduit à un comportement de "rate and state" sans l’introduction d’une variable interne. Nos conclusions sur le rôle de la pressurisation thermique pendant le cisaillement de fault gouge sont en accord qualitatif avec les nouveaux résultats expérimentaux disponibles. Enfin, sur la base des résultats numériques, nous étudions les hypothèses du modèle actuel de glissement sur un plan mathématique proposent à la littérature. Le rôle des conditions aux limites et du mode de localisation des déformations dans l’évolution du frottement de la faille pendant le glissement sismique. Le cas d’un domaine délimité et d’un mode de localisation de la déformation en mouvement est examiné dans le contexte d’un glissement sur un plan mathématique sous pressurisation thermique. Nos résultats étoffent le modèle original dans un contexte plus généralDuring coseismic slip, the energy released by the elastic unloading of the adjacent earth blocks can be separated in three main parts: The energy that is radiated to the earth’s surface (_ 5% of the whole energy budget), the fracture energy for the creation of new fault surfaces and finally, the energy dissipated inside a region of the fault, with finite thickness, which is called the fault gauge. This region accumulates the majority of the seismic slip. Estimating correctly the width of the fault gauge is of paramount importance in calculating the energy dissipated during the earthquake, the fault’s frictional response, and the conditions for nucleation of the fault in the form of seismic or aseismic slip.In this thesis different regularization approaches were explored for the estimation of the localization width of the fault’s principal slip zone during coseismic slip. These include the application of viscosity and multiphysical couplings in the classical Cauchy continuum, and the introduction of a first order micromorphic Cosserat continuum. First, we focus on the role of viscous regularization in the context of dynamical analyses, as a method for regularizing strain localization. We study the dynamic case for a strain softening strain-rate hardening classical Cauchy continuum, and by applying the Lyapunov stability analysis we show that introduction of viscosity is unable to prevent strain localization on a mathematical plane and mesh dependence.We perform fully non linear analyses using the Cosserat continuum under large seismic slip displacements of the fault gouge in comparison to its width. Cosserat continuum provides us with a proper account of the energy dissipated during an earthquake and the role of the microstructure in the evolution of the fault’s friction. We focus on the influence of the seismic slip velocity to the weakening mechanism of thermal pressurization. We notice that the influence of the boundary conditions in the diffusion of the pore fluid inside the fault gouge, leads to frictional strength regain after initial weakening. Furthermore, a traveling strain localization mode is present during shearing of the layer introducing oscillations in the frictional response. Such oscillations increase the spectral content of the earthquake. Introduction of viscosity in the above mode, leads to a rate and state behavior without the introduction of a specific internal state variable. Our conclusions about the role of thermal pressurization during shearing of the fault gouge, agree qualitatively with newly available experimental results.Finally, based on the numerical findings we investigate the assumptions of the current model of a slip on a mathematical plane, in particular the role of the boundary conditions and strain localization mode in the evolution of the fault’s friction during coseismic slip. The case of a bounded domain and a traveling strain localization mode are examined in the context of slip on a mathematical plane under thermal pressurization. Our results expand the original model in a more general context
18
Valmorbida, Giorgio. "Estabilidade de sistemas com atraso : analise de incertezas e de saturação empregando desigualdades matriciais lineares." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261833.
Full textAbstract:
Orientador: Pedro Luis Dias PeresDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
Made available in DSpace on 2018-08-06T06:53:10Z (GMT). No. of bitstreams: 1 Valmorbida_Giorgio_M.pdf: 1105118 bytes, checksum: 1fec640e2bfaeb6dac37afed313255ef (MD5) Previous issue date: 2006
Resumo: Este trabalho apresenta resultados no contexto de estabilidade de sistemas com atraso. A estabilidade de sistemas incertos com atraso é estudada utilizando o Teorema do Pequeno Ganho Escalonado a partir de um sistema de comparação. Aplicando resultados do Lema de Finsler e empregando matrizes de Lyapunov dependentes de parâmetro nas desigualdades matriciais lineares do Teorema do Pequeno Ganho, são obtidas condições independentes e condições dependentes do atraso para sistemas incertos. Sistemas com atraso que apresentam entrada com saturação em posição são estudados visando obter condições para cômputo de ganhos de realimentação de estados e visando obter uma estimativa para a região de atração do sistema em malha fechada. É considerada uma lei de controle com realimentação do estado atual e do estado atrasado. Funcionais de Lyapunov-Krasovskii são utilizados na obtenção das condições de estabilizabilidade. A maximização das estimativas das regiões de atração é feita a partir da solução de problemas de otimizaçã.o com restrições na forma de desigualdades matriciais lineares
Abstract: This work presents results in the context of time-delay system stability. Uncertain time-delay systems are studied by means of the Scaled Small-Gain Theorem. By applying results from Finsler's Lemma and using parameter-dependent Lyapunov matrices, delay-dependent and delay-independent conditions for uncertain systems are obtained in terms of linear matrix inequalities. Time-delay system presenting amplitude-saturating inputs are analyzed aiming to establish conditions to compute state-feedback gains and to obtain an estimate of the bassin of attraction of the system. A control law composed by a current state-feedback and a delayed state-feedback is considered. Lyapunov-Krasovskii functionals are the starting point to obtain the stabilizability conditions. The maximization the estimates of the bassin of attraction is carried out by solving an optimization problem whose constraints are linear matrix inequalities
Mestrado
Automação
Mestre em Engenharia Elétrica
19
Lacerda, Márcio Júnior 1987. "Contribuições ao problema de filtragem H-infinito para sistemas dinâmicos." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261059.
Full textAbstract:
Orientadores: Pedro Luis Dias Peres, Ricardo Coração de Leão Fontoura de OliveiraTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação
Made available in DSpace on 2018-08-25T15:07:40Z (GMT). No. of bitstreams: 1 Lacerda_MarcioJunior_D.pdf: 1206868 bytes, checksum: c5abb83323581461eb40c95f27c95097 (MD5) Previous issue date: 2014
Resumo: Este trabalho apresenta novas condições na forma de desigualdades matriciais lineares para o projeto de filtros H-infinito de ordem completa em três diferentes contextos: i) sistemas lineares incertos discretos com um atraso variante no tempo afetando os estados; ii) sistemas lineares com parâmetros variantes no tempo, contínuos e discretos, sujeitos a incertezas nas medições dos parâmetros; iii) sistemas não lineares quadráticos contínuos e discretos no tempo. Para cada contexto, o objetivo é projetar filtros: i) com termos atrasados nos estados; ii) dependentes dos parâmetros incertos medidos; iii) com termos quadráticos. Em cada um dos casos, o ponto de partida é a existência de uma função de Lyapunov que assegure estabilidade e um limitante para a norma H-infinito do sistema aumentado, ou seja, o sistema original conectado com o filtro de ordem completa. As condições de projeto são obtidas impondo-se uma determinada estrutura para as variáveis de folga, resultando em desigualdades matriciais com parâmetros escalares. A eficácia das condições apresentadas é ilustrada por meio de comparações numéricas utilizando exemplos da literatura
Abstract: This work presents new conditions in the form of linear matrix inequalities for full order H-infinity filter design in three different contexts: i) uncertain linear discrete-time systems with a time-varying delay affecting the states ii) linear parameter-varying systems, continuous and discrete-time, subject to inexactly measured parameters; iii) continuous and discrete-time nonlinear quadratic systems. For each context, the aim is to design filters: i) with state-delayed terms; ii) dependent upon the inexactly measured parameters; iii) with quadratic terms. In each case, the starting point is the existence of a Lyapunov function that assures stability and a bound to the H-infinity norm of the augmented system, that is, the original system conected with the full order filter. The design conditions are obtained by imposing a given structure to the slack variables, resulting in matrix inequalities with scalar parameters. The effectiveness of the proposed conditions is illustrated by means of numerical comparisons and benchmark examples from the literature
Doutorado
Automação
Doutor em Engenharia Elétrica
20
Volyanskyy, Kostyantyn. "Adaptive and neuroadaptive control for nonnegative and compartmental dynamical systems." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/34806.
Full textAbstract:
Neural networks have been extensively used for adaptive system identification as well as adaptive and neuroadaptive control of highly uncertain systems. The goal of adaptive and neuroadaptive control is to achieve system performance without excessive reliance on system models. To improve robustness and the speed of adaptation of adaptive and neuroadaptive controllers several controller architectures have been proposed in the literature. In this dissertation, we developed a new neuroadaptive control architecture for nonlinear uncertain dynamical systems as well as nonlinear nonnegative uncertain dynamical systems.
Nonnegative systems are essential in capturing the behavior of a wide range of dynamical systems involving dynamic states whose values are nonnegative. A subclass of nonnegative dynamical systems are compartmental systems. These systems are derived from mass and energy balance considerations and are comprised of homogeneous interconnected microscopic subsystems or compartments which exchange variable quantities of material via intercompartmental flow laws. In this research, we developed a direct adaptive and neuroadaptive control framework for stabilization, disturbance rejection and noise suppression for nonnegative and compartmental dynamical systems with exogenous system disturbances. Furthermore, we developed a new neuroadaptive control architecture for nonlinear uncertain dynamical systems. Specifically, the proposed framework involves a new and novel controller architecture involving additional terms, or Q-modification terms, in the update laws that are constructed using a moving time window of the integrated system uncertainty. The Q-modification terms can be used to identify the ideal neural network system weights which can be used in the adaptive law. In addition, these terms effectively suppress system uncertainty.
Finally, neuroadaptive output feedback control architecture for nonlinear nonnegative dynamical systems with input amplitude and integral constraints is developed. This architecture is used to control lung volume and minute ventilation with input pressure constraints that also accounts for spontaneous breathing by the patient. Specifically, we develop a pressure- and work-limited neuroadaptive controller for mechanical ventilation based on a nonlinear multi-compartmental lung model. The control framework does not rely on any averaged data and is designed to automatically adjust the input pressure to the patient's physiological characteristics capturing lung resistance and compliance modeling uncertainty. Moreover, the controller accounts for input pressure constraints as well as work of breathing constraints. The effect of spontaneous breathing is incorporated within the lung model and the control framework.
21
Djema, Walid. "Understanding cell dynamics in cancer from control and mathematical biology standpoints : particular insights into the modeling and analysis aspects in hematopoietic systems and leukemia." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS470.
Full textAbstract:
Cette thèse porte sur la modélisation et l’analyse de stabilité de certains mécanismes biologiques complexes en rapport avec le cancer. Un intérêt particulier est porté au cas de l’hématopoïèse et de la leucémie aiguë myéloblastique (LAM). Les modèles utilisés et/ou introduits dans cette thèse se décrivent par des équations aux dérivées partielles structurées en âge, qui se réduisent à des systèmes à retards de plusieurs types (retards ponctuels ou distribués, à support fini ou infini). Ces modèles à retards sont parfois couplés à des équations aux différences, et possiblement avec des paramètres variant dans le temps. Un des principaux challenges dans ce travail consiste à développer des méthodes temporelles, qui se basent sur la construction de fonctionnelles de Lyapunov-Krasovskii strictes, pour les systèmes non-linéaires à retards étudiés. Les principales notions abordées dans ces travaux incluent : l’analyse de stabilité/stabilisation et de robustesse, l’emploi de techniques de modélisation des populations cellulaires saines et malades, l’étude de différentes classes de systèmes dynamiques, (possiblement à temps variant ou à commutation), et également l’introduction de quelques outils issus de l’intelligence artificielle (planification et recherche de solution) dans un contexte de modèles biologiques. Ainsi, les méthodes de modélisation et d’analyse employées dans ce travail ont permis d’une part d’étendre les résultats de stabilité de cette classe de systèmes biologiques, et d’autre part de mieux comprendre certains mécanismes biologiques liés au cancer et sa thérapie. Plus précisément, certains concepts récemment établis en biologie et en médecine sont mis en évidence dans ce travail pour la première fois dans cette classe de systèmes, telles que : la dédifférenciation des cellules (plasticité), ou encore la dormance des cellules cancéreuses dans des modèles tenant compte de la cohabitation entre cellules saines et mutées. Les résultats obtenus sont interprétés dans le cas de l’hématopoïèse et de la LAM, mais ce travail s’applique également à d’autres types de tissus où le cycle cellulaire se produit de façon similaireMedical research is looking for new combined targeted therapies against cancer. Our research project -which involves intensive collaboration with hematologists from Saint-Antoine Hospital in Paris- is imbued within a similar spirit and fits the expectations of a better understanding of the behavior of blood cell dynamics. In fact, hematopoiesis provides a paradigm for studying all the mammalian stem cells, as well as all the mechanisms involved in the cell cycle. We address multiple issues related to the modeling and analysis of the cell cycle, with particular insights into the hematopoietic systems. Stability features of the models are highlighted, since systems trajectories reflect the most prominent healthy or unhealthy behaviors of the biological process under study. We indeed perform stability analysis of systems describing healthy and unhealthy situations, with a particular interest in the case of acute myeloblastic leukemia (AML). Thus, we pursue the objectives of understanding the interactions between the various parameters and functions involved in the mechanisms of interest. For that purpose, an advanced stability analysis of the cell fate evolution in treated or untreated leukemia is performed in several modeling frameworks, and our study suggests new anti-leukemic combined chemotherapy. Throughout the thesis, we cover many biological evidences that are currently undergoing intensive biological research, such as: cell plasticity, mutations accumulation, cohabitation between ordinary and mutated cells, control or eradication of cancer cells, cancer dormancy, etc.Among the contributions of Part I of the thesis, we can mention the extension of both modeling and analysis aspects in order to take into account a proliferating phase in which most of the cells may divide, or die, while few of them may be arrested during their cycle for unlimited time. We also introduce for the first time cell-plasticity features to the class of systems that we are focusing on.Next, in Part II, stability analyses of some differential-difference cell population models are performed through several time-domain techniques, including tools of Comparative and Positive Systems approaches. Then, a new age-structured model describing the coexistence between cancer and ordinary stem cells is introduced. This model is transformed into a nonlinear time-delay system that describes the dynamics of healthy cells, coupled to a nonlinear differential-difference system governing the dynamics of unhealthy cells. The main features of the coupled system are highlighted and an advanced stability analysis of several coexisting steady states is performed through a Lyapunov-like approach for descriptor-type systems. We pursue an analysis that provides a theoretical treatment framework following different medical orientations, among which: i) the case where therapy aims to eradicate cancer cells while preserving healthy ones, and ii) a less demanding, more realistic, scenario that consists in maintaining healthy and unhealthy cells in a controlled stable dormancy steady-state. Mainly, sufficient conditions for the regional exponential stability, estimate of the decay rate of the solutions, and subsets of the basins of attraction of the steady states of interest are provided. Biological interpretations and therapeutic strategies in light of emerging AML-drugs are discussed according to our findings.Finally, in Part III, an original formulation of what can be interpreted as a stabilization issue of population cell dynamics through artificial intelligence planning tools is provided. In that framework, an optimal solution is discovered via planning and scheduling algorithms. For unhealthy hematopoiesis, we address the treatment issue through multiple drug infusions. In that case, we determine the best therapeutic strategy that restores normal blood count as in an ordinary hematopoietic system
22
Silva, José Augusto Ignácio da. "Supressão robusta de ressonância de solo em helicóptero considerando incertezas estruturais, falha de atuador e não-linearidades concentradas /." Ilha Solteira, 2019. http://hdl.handle.net/11449/183184.
Full textAbstract:
Orientador: Gustavo Luiz Chagas Manhães de AbreuResumo: O presente trabalho propõe uma nova estratégia para supressão ativa robusta do fenômeno Ground Resonance (GR) em Helicópteros. O modelo clássico de análise deste fenômeno é desenvolvido para um rotor isotrópico e a análise de estabilidade é feita no domínio de Coleman, para encontrar as fronteiras de instabilidade. Também é proposta uma nova estratégia para lidar com essas fronteiras de instabilidade e suprimir o GR usando controladores com formulação descrita por conjuntos politópicos convexos. Controladores são projetados via desigualdades lineares matriciais (LMIs, Linear Matrix Inequalities), formulados de acordo com a Teoria de Estabilidade de Lyapunov. Adicionalmente, incertezas paramétricas na frequência de lead-lag das pás e a apresentação de uma falha estrutural nos atuadores são consideradas e, assim, novos controladores robustos são projetados a fim de expandir o envelope operacional da aeronave. Ainda, são considerados diferentes tipos de não-linearidades estruturais na rigidez e amortecimento do trem de pouso do helicóptero e a caracterização da estabilidade não-linear do sistema exibe oscilações em ciclo limite (LCO, Limit Cycle Oscillation), que são determinadas a partir da construção de Diagramas de Bifurcação. Utiliza-se a modelagem Fuzzy-TS do sistema para cada caso de estudo e, com base nas fronteiras de estabilidade não-linear do GR, definidas a partir dos Diagramas de Bifurcação, têm-se o projeto de controladores para supressão das LCOs do sistema. Os res... (Resumo completo, clicar acesso eletrônico abaixo)
Abstract: The present work proposes a new strategy for robust active suppression of Ground Resonance (GR) phenomenon in Helicopters. The classical model to analysis of this phenomenon is developed for an isotropic rotor and stability analysis is done in Coleman domain, to nd the boundaries of instability. It is also proposed a new strategy for dealing with these boundaries of instability and suppressing GR using controllers with polytopic convex hulls formulation. Controllers are designed via Linear Matrix Inequalities (LMIs), formulated according to the Lyapunov Stability Theory. Additionally, parametric uncertainties in the lead-lag frequency of the blades and actuators faults are considered and thus new robust controllers are designed to expand the aircraft operating envelope. Also, di erent types of structural nonlinearities in the landing gear sti ness and damping of the helicopter are considered, and the characterization of the nonlinear stability of the system exhibits Limit Cycle Oscillation (LCO), which are determined from the construction of Bifurcation Diagrams. Fuzzy-TS modeling is used for each case study and, based on the nonlinear stability boundaries of the GR, de ned from the Bifurcation Diagrams, the controllers to suppress the LCO are designed. The results of numerical simulations, discussions and conclusions are presented and show that the control strategy proposed is an attractive solution to suppress the linear and nonlinear GR problem, being able to expand the o... (Complete abstract click electronic access below)
Doutor
23
Mostefaoui, Imene Meriem. "Analyse mathématique d’un système dynamique/réaction-diffusion modélisant la distribution des bactéries résistantes aux antibiotiques dans les rivières." Thesis, La Rochelle, 2014. http://www.theses.fr/2014LAROS020/document.
Full textAbstract:
L'objectif de cette thèse est l'étude qualitative de certains modèles de la dynamique et la distribution des bactéries dans une rivière. Il s'agit de la stabilité des états stationnaires et l'existence des solutions périodiques. Nous considérons, dans la première partie de la thèse, un système d'équations différentielles ordinaires qui modélise les interactions et la dynamique de quatre espèces de bactéries dans une rivière. Nous avons étudié le comportement asymptotique des états stationnaires. L'étude de la stabilité des états stationnaires est essentiellement faite par la construction d'une fonction de Lyapunov combinée avec le principe d'invariance de LaSalle. D'autre part, l'existence des solutions périodiques est démontrée en utilisant le théorème de continuation de Mawhin. La deuxième partie de la thèse est consacrée à l'étude d'un système de convection-diffusion non-autonome. Ce modèle tient compte du transport des bactéries. Nous étudions l'analyse qualitative des solutions, nous déterminons l'ensemble limite du système et nous démontrons l'existence des états stationnaires positifs. L'étude de l'existence des états stationnaires (les seuls qu'il soit possible d'obtenir) est basée sur le théorème de Leray-SchauderThe objective of this thesis is the qualitative study of some models of the dynamic and the distribution of bacteria in a river. We are interested in the stability of equilibria and the existence of periodic solutions. The thesis can be divided into two parts; the first part is concerned with a mathematical analysis of a system of differential equations modelling the dynamics and the interactions of four species of bacteria in a river. The asymptotic behavior of equilibria is established. The stability study of equilibrium states is mainly done by construction of Lyapunov functions combined with LaSalle's invariance principle. On the other hand, the existence of periodic solutions is proved under certain conditions using the continuation theorem of Mawhin. In the second part of this thesis, we propose a non-autonomous convection-reaction diffusion system with nonlinear reaction source functions. This model refers to the quantification and the distribution of antibiotic resistant bacteria (ARB) in a river. Our main contributions are : (i) the determination of the limit set of the system; it is shown that it is reduced to the solutions of the associated elliptic system; (ii) sufficient conditions for the existence of a positive solution of the associated elliptic system based on the Leray Schauder's degree theory
24
Leite, Valter Junior de Souza. "Estudos sobre estabilidade robusta de sistemas lineares por meio de funções dependentes de parametros." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/260564.
Full textAbstract:
Orientador: Pedro Luis Dias PeresTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
Made available in DSpace on 2018-08-05T03:23:54Z (GMT). No. of bitstreams: 1 Leite_ValterJuniordeSouza_D.pdf: 4310851 bytes, checksum: bcd0414d19eb46e02496290857fdf9bc (MD5) Previous issue date: 2005
Resumo: Este trabalho trata da aplica¸c¿ao de funcionais de Lyapunov e Lyapunov-Krasovskii dependentes de parâmetro a alguns problemas selecionados da área de controle robusto, a saber: D-estabilidade robusta de polítipo de matrizes, D-estabilidade robusta de politopos de polinômios matriciais, estabilidade robusta de sistemas neutrais com atrasos variantes no tempo e controle robusto H8 de sistemas discretos no tempo com atraso nos estados. É utilizada a representação politópica para as incertezas dos sistemas estudados. São obtidas formulações convexas, na forma de desigualdades matriciais lineares, suficientes para a solução dos problemas selecionados. Essas condições podem ser resolvidas numericamente de maneira eficiente por meio de algoritmos especializados baseados em pontos interiores. Os resultados obtidos são menos conservadores que os encontrados na literatura, baseados em geral na estabilidade quadrática, isto é, as matrizes dos funcionais são fixas e independentes da incerteza
Abstract: This work deals with the application of parameter dependent Lyapunov and Lyapunov-Krasovskii functionals to some selected problems of robust control: robust D-stability of polytopes of matrices, robust D-stability of polytopes of polynomial matrices, robust stability of uncertain neutral systems with timevarying delays and robust H8 control of uncertain discrete time delay systems. The polytopic representation is used to describe the uncertainties. Convex formulations are obtained, in terms of inear matrix inequalities, that are sufficient for the solution of the selected problems. Those conditions can be solved in a efficient way through specialized interior point algorithms. The obtained results are less conservative than those from the literature, in general based on quadratic stability, i.e., the matrices in the functionals are fixed and do not depend on the uncertainty
Doutorado
Automação
Doutor em Engenharia Elétrica
25
Nersesov, Sergey G. "Nonlinear Impulsive and Hybrid Dynamical Systems." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7147.
Full textAbstract:
Modern complex dynamical systems typically possess a
multiechelon hierarchical hybrid structure characterized by
continuous-time dynamics at the lower-level units and logical
decision-making units at the higher-level of hierarchy. Hybrid
dynamical systems involve an interacting countable collection of
dynamical systems defined on subregions of the partitioned state
space. Thus, in addition to traditional control systems, hybrid
control systems involve supervising controllers which serve to
coordinate the (sometimes competing) actions of the lower-level
controllers. A subclass of hybrid dynamical systems are impulsive
dynamical systems which consist of three elements, namely, a
continuous-time differential equation, a difference equation, and
a criterion for determining when the states of the system are to
be reset. One of the main topics of this dissertation is the
development of stability analysis and control design for impulsive
dynamical systems. Specifically, we generalize Poincare's
theorem to dynamical systems possessing left-continuous flows to
address the stability of limit cycles and periodic orbits of
left-continuous, hybrid, and impulsive dynamical systems. For
nonlinear impulsive dynamical systems, we present partial
stability results, that is, stability with respect to part of the
system's state. Furthermore, we develop adaptive control framework
for general class of impulsive systems as well as energy-based
control framework for hybrid port-controlled Hamiltonian systems.
Extensions of stability theory for impulsive dynamical systems
with respect to the nonnegative orthant of the state space are
also addressed in this dissertation. Furthermore, we design
optimal output feedback controllers for set-point regulation of
linear nonnegative dynamical systems. Another main topic that has
been addressed in this research is the stability analysis of
large-scale dynamical systems. Specifically, we extend the theory
of vector Lyapunov functions by constructing a generalized
comparison system whose vector field can be a function of the
comparison system states as well as the nonlinear dynamical system
states. Furthermore, we present a generalized convergence result
which, in the case of a scalar comparison system, specializes to
the classical Krasovskii-LaSalle invariant set theorem. Moreover,
we develop vector dissipativity theory for large-scale dynamical
systems based on vector storage functions and vector supply rates.
Finally, using a large-scale dynamical systems perspective, we
develop a system-theoretic foundation for thermodynamics.
Specifically, using compartmental dynamical system energy flow
models, we place the universal energy conservation, energy
equipartition, temperature equipartition, and entropy
nonconservation laws of thermodynamics on a system-theoretic
basis.
26
Alvarez, Jarquin Nohemi. "Consensus variant dans le temps : application à la formation de véhicles." Thesis, Paris 11, 2015. http://www.theses.fr/2015PA112092/document.
Full textAbstract:
Les multiples applications liées aux systèmes multi-agents en réseau, tels que les satellites en formation, les oscillateurs couplés, les véhicules aériens sans pilote, entre autres, ont été, sans aucun doute, une motivation majeure dans le développement de cette thèse, qui est consacrée à l’étude du consensus de systèmes dynamiques et à la commande en formation de robots mobiles non holonomes. Dans le contexte du consensus, nous étudions la topologie en anneau avec de liens de communication variant dans le temps. Notamment, la communication peut être perdue pendant de longs intervalles de temps. Nous donnons de conditions suffisantes pour le consensus qui restent simples à vérifier, par exemple, en utilisant le théorème du petite gain. En suite, nous abordons le problème de consensus en supposant que la topologie de communication est variable. Nous établissons que le consensus est atteint à condition qu’il existe toujours un chemin de communication du type « spanning-tree » pendant un temps de séjour minimal. L'analyse s'appuie sur la théorie de stabilité des systèmes variant dans le temps et les systèmes à commutation. Dans le contexte de la commande en formation de véhicules autonomes nous adressons le problème de commande en suivi de trajectoire sur ligne droite en suivant une approche type maître-esclave. Nous montrons que le suivi global peut être obtenu à partir d’un contrôleur qui possède la propriété d’excitation persistante. En gros, le mécanisme de stabilisation dépend de l’excitation du système par une quantité qui est proportionnelle à l’erreur de suivi. Ensuite, la méthode est utilisée pour résoudre le problème de suivi de formation de plusieurs véhicules interconnectés sur la base d’une topologie « spanning-tree ». Nous donnons des conditions de stabilité concernant les modèles cinématique et dynamique, en utilisant la seconde méthode de LyapunovThe multiple applications related to networked multi-agent systems such as satellite formation flying, coupled oscillators, air traffic control, unmanned air vehicles, cooperative transport, among others, has been undoubtedly a watershed for the development of this thesis. The study of cooperative control of multi-agent systems is of great interest for his extensive field work and applications. This thesis is devoted to the study of consensus seeking of multi-agents systems and trajectory tracking of nonholonomic mobile robots.In the context of consensus seeking, first we study a ring topology of dynamic agents with time-dependent communication links which may disconnect for long intervals of time. Simple checkable conditions are obtained by using small-gain theorem to guarantee the achievement of consensus. Then, we deal with a network of dynamic agents with time-dependent communication links interconnected over a time-varying topology. We establish that consensus is reached provided that there always exists a « spanning-tree » for a minimal dwell-time by using stability theory of time-varying and switched systems. In the context of trajectory tracking, we investigate a simple leader-follower tracking controller for autonomous vehicles following straight lines. We show that global tracking may be achieved by a controller which has a property of persistency of excitation tailored for nonlinear systems. Roughly speaking the stabilisation mechanism relies on exciting the system by an amount that is proportional to the tracking error. Moreover, the method is used to solve the problem of formation tracking of multiple vehicles interconnected on the basis of a « spanning-tree » topology. We derive stability conditions for the kinematic and dynamic model by using a Lyapunov approach
27
Chen, Zengshi. "Dynamics and control of collision of multi-link humanoid robots with a rigid or elastic object." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1158442034.
Full text
28
Khansah, Hael. "Sur la commande de systèmes non linéaires par gains robustes séquencés." Phd thesis, Université Paul Sabatier - Toulouse III, 2007. http://tel.archives-ouvertes.fr/tel-00168054.
Full textAbstract:
Dans ce travail, nous avons développé une approche systématique traitant un problème particulier dans le domaine de la commande non linéaire. Il concerne le fait d'assurer une transition stable entre deux points opérationnels d'un système non linéaire. Cette approche emploie la stratégie de séquencement de gain et la notion d'incertitude bornée en norme pour approximer un système non linéaire à travers une famille de systèmes linéaires incertains à incertitude bornée en norme. Autour d'un ensemble de points d'équilibre, des lois de commande locale sont déterminées en garantissant quelques spécifications de performances locales. Le séquencement est déterminé de sorte que la stabilité est garantie. Par interpolation polynômiale continue, une loi de commande continue est établie à partir des points d'équilibre trouvés hors ligne et des correcteurs associés. Une stratégie de commande séquencée par retour d'état ainsi qu'une stratégie par retour de sortie dynamique ont été envisagées. Dans le premier cas, la commutation est faite lorsque l'état se trouve dans le bassin d'attraction du point d'équilibre ultérieur visé. Dans le deuxième, nous avons déterminé une loi de commande par retour de sortie dynamique o'u la politique de commutation est basée sur les états éstimés. Quelques exemples ont été donnés pour montrer l'efficacité de la méthode proposée.
29
Almér, Stefan. "Control and Analysis of Pulse-Modulated Systems." Doctoral thesis, KTH, Optimeringslära och systemteori, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4713.
Full textAbstract:
The thesis consists of an introduction and four appended papers. In the introduction we give an overview of pulse-modulated systems and provide a few examples of such systems. Furthermore, we introduce the so-called dynamic phasor model which is used as a basis for analysis in two of the appended papers. We also introduce the harmonic transfer function and finally we provide a summary of the appended papers. The first paper considers stability analysis of a class of pulse-width modulated systems based on a discrete time model. The systems considered typically have periodic solutions. Stability of a periodic solution is equivalent to stability of a fixed point of a discrete time model of the system dynamics. Conditions for global and local exponential stability of the discrete time model are derived using quadratic and piecewise quadratic Lyapunov functions. A griding procedure is used to develop a systematic method to search for the Lyapunov functions. The second paper considers the dynamic phasor model as a tool for stability analysis of a general class of pulse-modulated systems. The analysis covers both linear time periodic systems and systems where the pulse modulation is controlled by feedback. The dynamic phasor model provides an $\textbf{L}_2$-equivalent description of the system dynamics in terms of an infinite dimensional dynamic system. The infinite dimensional phasor system is approximated via a skew truncation. The truncated system is used to derive a systematic method to compute time periodic quadratic Lyapunov functions. The third paper considers the dynamic phasor model as a tool for harmonic analysis of a class of pulse-width modulated systems. The analysis covers both linear time periodic systems and non-periodic systems where the switching is controlled by feedback. As in the second paper of the thesis, we represent the switching system using the L_2-equivalent infinite dimensional system provided by the phasor model. It is shown that there is a connection between the dynamic phasor model and the harmonic transfer function of a linear time periodic system and this connection is used to extend the notion of harmonic transfer function to describe periodic solutions of non-periodic systems. The infinite dimensional phasor system is approximated via a square truncation. We assume that the response of the truncated system to a periodic disturbance is also periodic and we consider the corresponding harmonic balance equations. An approximate solution of these equations is stated in terms of a harmonic transfer function which is analogous to the harmonic transfer function of a linear time periodic system. The aforementioned assumption is proved to hold for small disturbances by proving the existence of a solution to a fixed point equation. The proof implies that for small disturbances, the approximation is good. Finally, the fourth paper considers control synthesis for switched mode DC-DC converters. The synthesis is based on a sampled data model of the system dynamics. The sampled data model gives an exact description of the converter state at the switching instances, but also includes a lifted signal which represents the inter-sampling behavior. Within the sampled data framework we consider H-infinity control design to achieve robustness to disturbances and load variations. The suggested controller is applied to two benchmark examples; a step-down and a step-up converter. Performance is verified in both simulations and in experiments.QC 20100628
30
Safi, Mohammed. "Stabilité de Lyapunov de systèmes couplés impliquant une équation de transport." Thesis, Toulouse, ISAE, 2018. http://www.theses.fr/2018ESAE0022/document.
Full textAbstract:
L’objet de cette thèse est l’étude des propriétés de stabilité et contrôle pour des systèmes linéaires écrits à l’aide d’équations aux dérivées partielles (EDP) ou d’équations à retard. Nous souhaitons exploiter dans cette thèse les liens qui existent entre ces deux classes de systèmes de dimension infinie afin de développer une nouvelle approche permettant leur analyse. En effet dans plusieurs applications, il est possible de choisir l’un ou l’autre de ces deux types de systèmes pour modéliser la dynamique considérée. Par exemple, les phénomènes de congestion dans un réseau routier peuvent être modélisés à l’aide d’EDP de type transport [JKC], mais aussi par un modèle à retard distribué [MMN] ou encore à retard discret [SN]. On peut également renvoyer aux travaux de Krstic [K] sur la formulation d’un système à retard comme un système EDP. Ces deux classes de systèmes sont des cas particuliers de systèmes de dimension infinie, et contrairement aux cas de systèmes de dimension finie, on parle de fonctions d’état plutôt que vecteur d’état. Cela implique que l’analyse associée est plus délicate et fait appel à des outils dédiés. Dans le cadre de la thèse, l’étudiant se focalisera sur les approches basées sur une extension du théorème de Lyapunov pour les systèmes de dimension infinie utilisant des fonctionnelles spécifiques. Comme pour la modélisation, l’analyse de stabilité des systèmes à retard ou de type EDP peut être menée à l’aide de fonctionnelles de Lyapunov très similaires. Nous souhaitons que cette thèse tire parti des travaux existants dans les deux communautés sur les systèmes à retards et de type EDP pour développer une approche novatrice et unifiée pour l’analyse et le contrôle de systèmes de dimension infinie. Pour cela, le candidat s’appuiera sur ses acquis en automatique et en mathématiques ainsi que sur l’expertise des deux encadrants. Plusieurs contributions sont attendues durant la thèse. Dans un premier temps, il sera question d’étendre des résultats récents [SG1,2] développés pour l’analyse de stabilité des systèmes à retards au cas de systèmes régis par des EDP. Ces premiers résultats auront vocation à servir de base pour l’étude de la synthèse de commandes robustes dans le cadre d’applications telles que le contrôle de trafic routier [MMN], le contrôle de vibration [RBPA], etc… Cette thèse en automatique requiert plusieurs compétences parmi lesquelles des connaissances sur la théorie de Lyapunov pour les systèmes avec ou sans retard, sur les inégalités matricielles linéaires tout en s’appuyant sur les outils de mathématiques appliquées pour l’étude des équations aux dérivées partielles (algèbre linéaire, analyse fonctionnelle, espaces de Hilbert, de Sobolev)The purpose of this thesis is the study of stability and control properties for linear systems described by partial differential equations (PDE) or delay differential equations. We wish to use in this thesis the relationship between these two classes of infinite-dimensional systems in view of developing a new paradigm for their analysis. Indeed, in many applications, it is possible to choose one or the other of these two classes of systems to model the dynamics of the system under consideration. For example, traffic flow can be modeled using PDE type of transportation [JKC], but also by a distributed delay model [SMP] or discrete delay [SN]. We may also refer to the work of Krstic [K] on the formulation of a delay system as an PDE system. These two classes of systems are special cases of infinite dimensional systems, unlike the case of finite-dimensional systems, we better called state functions rather than the state vector. This implies that the analysis is more delicate and refers to the use of dedicated tools. As part of the thesis, the student will focus on approaches based on an extension of Lyapunov theorem for infinite dimensional systems using specific functional. As for the modeling process, the stability analysis of delayed or PDE type systems can be conducted using very similar Lyapunov functionals. We hope that this thesis builds on existing work in the two communities on delay systems and PDE to develop an innovative and unified approach to the analysis and control of infinite dimensional systems. To do so, the candidate will build on its skills in automatic and mathematics as well as the on from expertise of both supervisors. Several contributions are expected during the thesis . Initially, we aim at extedning recent results [SG13,14] developed in the context of the stability analysis of delay systems to the case of systems governed by PDE. These first results will provide the basis for the design of robust control laws for various applications including traffic control, vibration control, etc ... Cette thèse portera sur l’étude des propriétés de stabilité et de contrôle des systèmes linéaires de dimension infinie, plus particulièrement écrits à l’aide d’EDP ou d’équations à retard. L’intérêt naturel pour l’étude de cette classe de systèmes à la frontière entre mathématiques appliquées et automatique connaît un succès grandissant de part la large gamme d’applications en contrôle pouvant être décrites par ces modèles : en ingénierie, biologie, informatique… L’émulation scientifique entre systèmes à retard et systèmes de type EDP permettra en outre à cette thèse de tirer parti des méthodes et outils propres à chacun des ces domaines. This PhD proposal in automatic control requires several skills including knowledge on Lyapunov theory for systems with or without delay , on linear matrix inequalities while relying on mathematical tools applied in the study of partial differential equations ( linear algebra functional analysis , Hilbert spaces , Sobolev)
31
Djaneye-Boundjou, Ouboti Seydou Eyanaa. "Particle Swarm Optimization Stability Analysis." University of Dayton / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=dayton1386413941.
Full text
32
Silveira, Hector Bessa. "Formas triangulares para sistemas não-lineares com duas entradas e controle de sistemas sem arrasto em SU(n) com aplicações em mecânica quântica." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/3/3139/tde-13082010-163547/.
Full textAbstract:
A presente tese aborda dois problemas distintos e independentes: triangularização de sistemas não-lineares com duas entradas e controle de sistemas sem arrasto que evoluem no grupo especial unitário SU(n). Em relação ao primeiro, estabeleceu-se, através da generalização de resultados bem conhecidos, condições geométricas para que um sistema com duas entradas seja descrito por uma forma triangular específica após uma mudança de coordenadas e uma realimentação de estado estática regular. Para o segundo problema, desenvolveu-se uma estratégia de controle que força o estado do sistema a rastrear assintoticamente uma trajetória de referência periódica que passa por um estado objetivo arbitrário. O método de controle proposto utiliza os resultados de convergência de tipo- Lyapunov que foram estabelecidos pela presente pesquisa e que tiveram como inspiração uma versão periódica do princípio da invariância de LaSalle. Apresentou-se, ainda, os resultados de simulação obtidos com a aplicação da técnica de controle desenvolvida a um sistema quântico consistindo de duas partículas de spin-1/2, com o objetivo de gerar a porta lógica quântica C-NOT.This thesis treats two distinct and independent problems: triangularization of nonlinear systems with two inputs and control of driftless systems which evolve on the special unitary group SU(n). Concerning the first, one has established, by means of the generalization of well-known results, geometric conditions for a system with two inputs to be described by a specific triangular form after a change of coordinates and a regular static state feedback. For the second problem, one has developed a control strategy that forces the state of the system to track in an asymptotic manner a periodic reference trajectory which passes by an arbitrary goal state. The proposed control method uses Lyapunovlike convergence results that were established in this research and which were inspired in a periodic version of LaSalles invariance principle. Furthermore, one has shown the simulation results obtained from the application of the developed control technique to a quantum system consisting of two spin-1/2 particles, with the aim of generating the C-NOT quantum logic gate.
33
Hassan, Lama. "Observation et commande des systèmes non linéaires à retard." Phd thesis, Université de Lorraine, 2013. http://tel.archives-ouvertes.fr/tel-00934943.
Full textAbstract:
L'objectif de cette thèse est de développer des méthodes de synthèses d'observateurs et des contrôleurs basés sur un observateur pour les systèmes à retard. Différentes classes de systèmes ont été traitées avec différents types de retard. Trois méthodes ont été développées. La première méthode traite des systèmes non linéaires avec des non-linéarités lipschitziennes et consiste à transformer le système d'origine à un système LPV grâce à une reformulation de la propriété classique de Lipschitz. Cette technique est formulée pour les cas continu et discret, respectivement. Nous avons démontré, à travers des exemples numériques, que cette technique offre des conditions de synthèse moins restrictives par rapport aux résultats existants dans la littérature. La seconde méthode est développée pour une classe de systèmes singuliers avec des perturbations. La principale difficulté résidait dans la présence des dérivées des perturbations qui entravent l'analyse de la stabilité et pour laquelle deux approches ont été proposées: une approche Hinf en utilisant une fonctionnelle de Lyapunov-Krasovskii spéciale dépendante des perturbations et une approche basée sur l'utilisation d'un critère de performance W1;2. La dernière méthode est basée sur l'utilisation des matrices de pondération libres pour résoudre le problème de contrôle des systèmes non-linéaires à retards inconnus. La solution proposée fournit une condition de synthèse LMI garantissant la stabilisation du système en boucle fermée malgré la présence du retard inconnu, au lieu d'une inégalité matricielle linéaire itérative ILMI trouvée habituellement dans la littérature.
34
La, Seta Piergiovanni. "Regelungstechnische Konzepte zur Integration alternativer Erzeugungsanlagen in lokale Energieversorgungsnetze unter besonderer Berücksichtigung der Systemstabilität." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2007. http://nbn-resolving.de/urn:nbn:de:swb:14-1195727596802-34238.
Full textAbstract:
In zukünftigen Elektroenergiesystemen wird die dezentrale, häufig auf erneuerbaren Quellen basierende Energieversorgung eine große Bedeutung einnehmen. Die wachsende Präsenz der dezentralen Erzeugung in verschiedenen Spannungsebenen des elektrischen Netzes erfordert neue Konzepte zur Regelung des elektrischen Energieversorgungssystems. Insbesondere gibt es eine Tendenz auch kleine Netzbereiche autonome, d.h. vom Verbundnetz unabhängig zu betreiben. In diesem Zusammenhang müssen die Stabilitäts- und Regelungsaspekte immer stärker berücksichtigt werden. Die vorliegende Untersuchung konzentriert sich auf die Beurteilung und die Verbesserung der Stabilität von Windkraftanlagen (WKA). Die Integration von WKA zur dezentralen Energieversorgung in lokale Energienetze unter besonderer Berücksichtigung der Systemsstabilität ist das Ziel dieser Arbeit. Hierfür muss die Analyse der Stabilität einer WKA sowohl qualitativ als auch quantitativ durchgeführt werden, um die Faktoren zu ermitteln, die zur Verbesserung der Systemsstabilität beitragen. Der darauf basierte Entwurf von Regelstrategien für ein verbessertes dynamisches und transientes Verhalten wird theoretisch und durch numerische Simulationen validiert.
35
La, Seta Piergiovanni. "Regelungstechnische Konzepte zur Integration alternativer Erzeugungsanlagen in lokale Energieversorgungsnetze unter besonderer Berücksichtigung der Systemstabilität." Doctoral thesis, Technische Universität Dresden, 2006. https://tud.qucosa.de/id/qucosa%3A23999.
Full textAbstract:
In zukünftigen Elektroenergiesystemen wird die dezentrale, häufig auf erneuerbaren Quellen basierende Energieversorgung eine große Bedeutung einnehmen. Die wachsende Präsenz der dezentralen Erzeugung in verschiedenen Spannungsebenen des elektrischen Netzes erfordert neue Konzepte zur Regelung des elektrischen Energieversorgungssystems. Insbesondere gibt es eine Tendenz auch kleine Netzbereiche autonome, d.h. vom Verbundnetz unabhängig zu betreiben. In diesem Zusammenhang müssen die Stabilitäts- und Regelungsaspekte immer stärker berücksichtigt werden. Die vorliegende Untersuchung konzentriert sich auf die Beurteilung und die Verbesserung der Stabilität von Windkraftanlagen (WKA). Die Integration von WKA zur dezentralen Energieversorgung in lokale Energienetze unter besonderer Berücksichtigung der Systemsstabilität ist das Ziel dieser Arbeit. Hierfür muss die Analyse der Stabilität einer WKA sowohl qualitativ als auch quantitativ durchgeführt werden, um die Faktoren zu ermitteln, die zur Verbesserung der Systemsstabilität beitragen. Der darauf basierte Entwurf von Regelstrategien für ein verbessertes dynamisches und transientes Verhalten wird theoretisch und durch numerische Simulationen validiert.
36
Mintsa, Mi Ondo Julie. "Les aspects spatiaux dans la modélisation en épidémiologie." Thesis, Grenoble, 2012. http://www.theses.fr/2012GRENS042/document.
Full textAbstract:
Dans cette thèse on s'intéresse a l'aspect spatial dans la modélisation en épidémiologie, ainsi que des conditions menant a la stabilité des systèmes que nous présentons, en épidémiologie, a partir des modèles classiques de Ross et Mckendrick. Dans un premier temps, nous examinons les effets de l'indice de la différence normalisée de végétation (NDVI) dans un modèle de contamination du paludisme a Bankoumana, une région du Mali. A partir du système obtenu, nous trouvons le taux de reproduction de base. Deux points d'équilibre sont déduits dont, un point d'équilibre sans maladie et un point d'équilibre endémique. Ce dernier point d'équilibre ainsi que le taux de reproduction de base sont fonction de l'indice de végétation normalisée. Par la suite, nous construisons un modèle ayant des équations a retard, dans lequel est également incorporée le NDVI. Le taux de reproduction de base ainsi que les deux points d'équilibre qui découlent de notre système sont fonction des retards introduits. Nous montrons que la stabilité de nos points d'équilibre est, non seulement fonction du taux de reproduction de base, mais elle est aussi étroitement liée aux retards introduits. Dans une autre optique, nous fractionnons la région d'étude en zones dans lesquelles nous émettons l'hypothèse que le taux de contagion induite par les individus d'une zone sur les individus de la même zone, ainsi que celui des individus d'une zone sur ceux d'une autre zone, peut être différents. Nous obtenons un système qui nous permet de déterminer les points d'équilibre ainsi que les conditions qui nous permettent d'obtenir la stabilité au sens de Lyapunov. Puis, nous perturbons le système précédent au niveau de son unique point d'équilibre endémique, en introduisant un bruit additif. Par suite, les conditions permettant la stabilité au sens de Lyapunov, sur le nouveau système obtenu, sont également déduites . Dans un cadre similaire, nous élaborons un modèle multi-groupes, dans lequel nous introduisons des coordonnées spatiales. Les groupes sont formés selon une proximité dépendant du rayon d'un cercle, de manière aléatoire. Ici, le taux de contagion est supposé uniforme dans les groupes. Après avoir déterminé les points d'équilibre ainsi que le taux de reproduction de base,nous trouvons les conditions qui favorisent la stabilité au sens de Lyapunov dans le cadre général. A l'ordre 1, c'est-a-dire, lorsqu'on suppose que nous n'avons qu'un groupe, les conditions de stabilité sont obtenus par le critère de Routh-HurwitzIn this thesis, our interest is on the aspect in space of the establishment of a spatial model in epidemiology and the conditions leading to the stability of the systems that we present, in epidemiology, from the classical models by Ross and Mckendrick. Firstly, we intend to examine the eects of the Normalized DiFerence Vegetation Index(NDVI) in a model of contamination of malaria in Bankoumana, a region in Mali. From the system obtained, we willnd the basic reproduction rate. Then we deduce two point of equilibrium, among which one point of equilibrium without the disease and another one with an endemic point. The latter with the basic reproduction rate vary according to the indices of normalized vegetation. Then, we will build a model having equations delay, containing the NDVI. The rate of basic reproduction and the two points of equilibrium that come from our system depend upon the delay introduced. We will show that the stability of our points of equilibrium is not only dependent upon the basic reproduction rate, but also closely related to the delays introduced. In another way, we will divide the region of study in areas where we will set hypotheses that the rate of contamination brought about by individuals in an area of study on the others, can be dierent. It will permit us to obtain a system in which we will determine the points of equilibrium and the conditions that will lead us to obtain the stability according to Lyapunov. Then, we will disturb the previous system at the level of its unique endemic point of equilibrium, with the introduction of an additional noise. The conditions leading to stability according to Lyapunov, on the new system obtained, are generally deduced here. In a similar framework, we will elaborate a multigroups model, in which we will introduce spatial coordinates. The groups are formed according to a closeness depending to a radius of a circle at random. Here, the rate of contamination is supposed to be uniform in the groups. After having determined the point of equilibrium and the rate of basic reproduction, we will nd the conditions facilitating stability in as by Lyapunov in a global framework. In the order1, it means that supposing that we have only one group, the conditions of stability are obtained according to the Routh-Hurvitz criteria
37
Valmorbida, Giorgio. "Analyse en stabilité et synthèse de lois de commande pour des systèmes polynomiaux saturants." Phd thesis, INSA de Toulouse, 2010. http://tel.archives-ouvertes.fr/tel-00512335.
Full textAbstract:
La classe des systèmes non-linéaires dont la dynamique est définie par un champ de vecteurs polynomial est étudié. Des modèles polynomiaux peuvent représenter différents systèmes réels ou bien definir des approximations plus riches que des modèles linéaires pour des systèmes non-linéaires différentiables. Des techniques de programmation semi-définie développées récemment ont rendu possible l'étude de cette classe de systèmes avec des outils numériques. Le problème d'analyse en stabilité locale est résolu via des conditions basées sur la positivité de polynomes. Dans le cadre de la synthèse de lois de commande nous proposons un changement de variables linéaire pour traiter la synthèse de lois de commande non-linéaire qui garantissent la stabilité locale. Les ensembles définissant des estimations de la région d'attraction, définis par des courbes de niveau de la fonction de Lyapunov pour le système, sont également donnés par des fonctions polynomiales.
38
Mazumder, Sudip K. "Nonlinear Analysis and Control of Standalone, Parallel DC-DC, and Parallel Multi-Phase PWM Converters." Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/28690.
Full textAbstract:
Applications of distributed-power systems are on the rise. They are already used in telecommunication power supplies, aircraft and shipboard power-distribution systems, motor drives, plasma applications, and they are being considered for numerous other applications. The successful operation of these multi-converter systems relies heavily on a stable design. Conventional analyses of power converters are based on averaged models, which ignore the fast-scale instability and analyze the stability on a reduced-order manifold. As such, validity of the averaged models varies with the switching frequency even for the same topological structure.
The prevalent procedure for analyzing the stability of switching converters is based on linearized smooth averaged (small-signal) models. Yet there are systems (in active use) that yield a non-smooth averaged model. Even for systems for which smooth averaged models are realizable, small-signal analyses of the nominal solution/orbit do not provide anything about three important characteristics: region of attraction of the nominal solution, dependence of the converter dynamics on the initial conditions of the states, and the post-instability dynamics. As such, converters designed based on small-signal analyses may be conservative. In addition, linear controllers based on such analysis may not be robust and optimal. Clearly, there is a need to analyze the stability of power converters from a different perspective and design nonlinear controllers for such hybrid systems.
In this Dissertation, using bifurcation analysis and Lyapunov's method, we analyze the stability and dynamics of some of the building blocks of distributed-power systems, namely standalone, integrated, and parallel converters. Using analytical and experimental results, we show some of the differences between the conventional and new approaches for stability analyses of switching converters and demonstrate the shortcomings of some of the existing results. Furthermore, using nonlinear analyses we attempt to answer three fundamental questions: when does an instability occur, what is the mechanism of the instability, and what happens after the instability?
Subsequently, we develop nonlinear controllers to stabilize parallel dc-dc and parallel multi-phase converters. The proposed controllers for parallel dc-dc converters combine the concepts of multiple-sliding-surface and integral-variable-structure control. They are easy to design, robust, and have good transient and steady-state performances. Furthermore, they achieve a constant switching frequency within the boundary layer and hence can be operated in interleaving or synchronicity modes. The controllers developed for parallel multi-phase converters retain many of the above features. In addition, they do not require any communication between the modules; as such, they have high redundancy. One of these control schemes combines space-vector modulation and variable-structure control. It achieves constant switching frequency within the boundary layer and a good compromise between the transient and steady-state performances.Ph. D.
39
Costa, de Oliveira Guacira. "Advances in multi-terminal HVDC transmission systems : nonlinear controllers for modular multilevel converters." Electronic Thesis or Diss., université Paris-Saclay, 2020. http://www.theses.fr/2020UPASG037.
Full textAbstract:
Le convertisseur modulaire à plusieurs niveaux est un sujet d'intérêt important et actuel dans le contexte des applications de systèmes de transmission haute tension à courant continu. Cette topologie convient à plusieurs applications, en raison de pertes de commutation plus faibles dues à une fréquence de commutation plus petite, à une faible distorsion harmonique de courant alternatif, à une structure modulaire permettant une construction évolutive, et une maintenance plus simple. Cependant, une stratégie de contrôle plus complexe est nécessaire pour contrôler le courant circulant, pour compenser le déséquilibre de tension entre les circuits et l'équilibrage de tension de SM, de manière à maintenir constantes les tensions des condensateurs de SM. Cette thèse présente deux contrôleurs non linéaires pour un MMC, capables de contrôler les courants circulants et l'énergie dans le convertisseur. Le premier est conçu selon la théorie bilinéaire basée sur le contrôle de rétroaction quadratique. Le deuxième contrôleur proposé est développé en utilisant la théorie de Lyapunov, fortement basé sur des techniques de perturbation singulière et de linéarisation par bouclage. Pour les deux, une étude mathématique est réalisée sur la stabilité, basée sur la théorie de Lyapunov. Ce résultat assure une stabilisation asymptotique pour les trois phases MMC. L'utilisation d'une fonction de Lyapunov implique une vérification formelle de la stabilité et une région explicite d'attraction pour le modèle considéré. Les deux techniques de contrôle sont développées à partir d'un modèle bilinéaire moyen, et la robustesse et les performances sont vérifiées au moyen d'un modèle de commutation MMC provenant des simulations électriques Matlab Simscape. L'évaluation comprend des variations de référence de puissance active et réactive, des conditions de déséquilibre du réseau, des incertitudes de paramètres et même une comparaison avec un contrôleur PI standard. Aussi, pour les contrôleurs non linéaires sont étudiés: l'effet des gains du contrôle sur la dynamique du système et les performances du contrôleur en cas de changement du point de fonctionnement. Les contributions principales de la thèse sont les deux algorithmes de contrôle non linéaires distincts, basés sur un modèle mathématique bilinéaire, conçus pour les convertisseurs MMC; Les deux algorithmes sont capables de contrôler l’équilibrage du courant et énergie du convertisseur au niveau du modèle détaillé du MMC par commutation; Il existe une analyse formelle de la stabilité par la théorie de Lyapunov pour ces systèmes; et une fois que le contrôle proposé n'est pas basé sur un modèle linéarisé, une vaste région d'opération est garantieMMC is a very important topic in the context of high voltage direct-current transmission systems applications. This topology is suitable for several applications, as a result of smaller switching losses due to lower switching frequency, low alternating-current harmonic distortion, modular structure enabling scalability construction and practical maintenance. However, a more complex control strategy is required to control circulating current, to compensate the voltage imbalance between legs and voltage balancing of SM, such as to maintain SM's capacitors voltages constant. This thesis presents two nonlinear controllers for an MMC, able to control circulating currents, and the energy in the converter. First proposed controller is developed using Lyapunov theory, strongly based on singular perturbation and feedback linearization techniques. Second one is designed following bilinear theory based on quadratic feedback control. For both, a mathematical proof is given for its stability, which is based on Lyapunov's theory. This result provides asymptotic stabilization for the three-phases MMC. The use of a Lyapunov function implies a formal verification of stability and a broad region of attraction for the considered model. Both control techniques are developed by means of an average bilinear model and performances are verified by means of a detailed MMC switching model at Matlab Simscape Electrical environment. The evaluation includes active and reactive power reference variations, grid imbalance conditions, parameters uncertainties and even a comparison with a standard PI controller. Also, for the nonlinear controllers, it is studied the effect of control gains on the system's dynamics. The main thesis' contributions can then be stated as the two distinct nonlinear control algorithms, based on a bilinear mathematical model, designed for MMC converters; Both algorithms are able to control circulating currents and converter's energy at the switching MMC model; There are formal stability analysis by Lyapunov theory for these controllers; and once these proposed controllers are not based on a linearized model, a broad operation region is obtained
Conversor multinível modular é o tópico de interesse amplo e atual no contexto de aplicações de sistemas de transmissão de corrente contínua de alta tensão. Essa topologia é adequada para várias aplicações, como resultado de menores perdas de chaveamento, devido à menor frequência de comutação dos IGBTs, baixa distorção harmônica na corrente alternada, estrutura modular que permite escalabilidade na construção e manutenção prática. No entanto, é necessária uma estratégia de contrôle mais complexa para controlar a corrente circulante, para compensar o desequilíbrio de tensão entre as pernas e o equilíbrio de tensão dos sub-módulos, de forma a manter constantes as tensões dos capacitores dos sub-módulos. Esta tese apresenta dois controles não-lineares para conversores MMC, capazes de controlar correntes circulantes e a energia no conversor. O primeiro é projetado seguindo a teoria bilinear baseada no controle de feedback quadrático. O segundo controlador proposto é desenvolvido usando a teoria de Lyapunov, fortemente baseada em técnicas singular perturbation e feedback linearization. Para ambos, é definida uma prova matemática de sua estabilidade, baseada na teoria de Lyapunov. Este resultado fornece estabilização assintotica para as três fases MMC. O uso de uma função de Lyapunov implica uma verificação formal da estabilidade e uma região explícita de atração para o modelo considerado. Ambas as técnicas de controle são desenvolvidas por meio de um modelo médio bilinear e a robustez e o desempenho são verificados por meio de um modelo chaveado de conversores MMC nas simulações do Matlab Simscape Electrical. A avaliação inclui variações de referência de potência ativa e reativa, condições de desequilíbrio da rede, incertezas de parâmetros e até uma comparação com um controlador PI. Além disso, para os controladores não lineares, são estudados: o efeito do controle de ganho na dinâmica do sistema e no desempenho do controlador em caso de alteração no ponto de operação. As principais contribuições da tese são os dois algoritmos distintos de controle não-linear, baseados em um modelo matemático bilinear, projetados para conversores MMC; Ambos os algoritmos são capazes de controlar o equilíbrio de corrente circulante e a energia do conversor; Há uma análise formal de estabilidade pela teoria de Lyapunov para esse sistema; e uma vez que os controles propostos não se baseiam em um modelo linearizado, uma vasta região de operação é alcançável
40
Rocha, Eugénio Alexandre Miguel. "Uma Abordagem Algébrica à Teoria de Controlo Não Linear." Doctoral thesis, Universidade de Aveiro, 2003. http://hdl.handle.net/10773/21444.
Full textAbstract:
Doutoramento em MatemáticaNesta tese de Doutoramento desenvolve-se principalmente uma abordagem algébrica à teoria de sistemas de controlo não lineares. No entanto, outros tópicos são também estudados. Os tópicos tratados são os seguidamente enunciados: fórmulas para sistemas de controlo sobre álgebras de Lie livres, estabilidade de um sistema de corpos rolantes, algoritmos para aritmética digital, e equações integrais de Fredholm não lineares. No primeiro e principal tópico estudam-se representações para as soluções de sistemas de controlo lineares no controlo. As suas trajetórias são representadas pelas chamadas séries de Chen. Estuda-se a representação formal destas séries através da introdução de várias álgebras não associativas e técnicas específicas de álgebras de Lie livres. Sistemas de coordenadas para estes sistemas são estudados, nomeadamente, coordenadas de primeiro tipo e de segundo tipo. Apresenta-se uma demonstração alternativa para as coordenadas de segundo tipo e obtêm-se expressões explícitas para as coordenadas de primeiro tipo. Estas últimas estão intimamente ligadas ao logaritmo da série de Chen que, por sua vez, tem fortes relações com uma fórmula designada na literatura por “continuous Baker-Campbell- Hausdorff formula”. São ainda apresentadas aplicações à teoria de funções simétricas não comutativas. É, por fim, caracterizado o mapa de monodromia de um campo de vectores não linear e periódico no tempo em relação a uma truncatura do logaritmo de Chen. No segundo tópico é estudada a estabilizabilidade de um sistema de quaisquer dois corpos que rolem um sobre o outro sem deslizar ou torcer. Constroem-se controlos fechados e dependentes do tempo que tornam a origem do sistema de dois corpos num sistema localmente assimptoticamente estável. Vários exemplos e algumas implementações em Maple°c são discutidos. No terceiro tópico, em apêndice, constroem-se algoritmos para calcular o valor de várias funções fundamentais na aritmética digital, sendo possível a sua implementação em microprocessadores. São também obtidos os seus domínios de convergência. No último tópico, também em apêndice, demonstra-se a existência e unicidade de solução para uma classe de equações integrais não lineares com atraso. O atraso tem um carácter funcional, mostrando-se ainda a diferenciabilidade no sentido de Fréchet da solução em relação à função de atraso.
In this PhD thesis several subjects are studied regarding the following topics: formulas for nonlinear control systems on free Lie algebras, stabilizability of nonlinear control systems, digital arithmetic algorithms, and nonlinear Fredholm integral equations with delay. The first and principal topic is mainly related with a problem known as the continuous Baker-Campbell-Hausdorff exponents. We propose a calculus to deal with formal nonautonomous ordinary differential equations evolving on the algebra of formal series defined on an alphabet. We introduce and connect several (non)associative algebras as Lie, shuffle, zinbiel, pre-zinbiel, chronological (pre-Lie), pre-chronological, dendriform, D-I, and I-D. Most of those notions were also introduced into the universal enveloping algebra of a free Lie algebra. We study Chen series and iterated integrals by relating them with nonlinear control systems linear in control. At the heart of all the theory of Chen series resides a zinbiel and shuffle homomorphism that allows us to construct a purely formal representation of Chen series on algebras of words. It is also given a pre-zinbiel representation of the chronological exponential, introduced by A.Agrachev and R.Gamkrelidze on the context of a tool to deal with nonlinear nonautonomous ordinary differential equations over a manifold, the so-called chronological calculus. An extensive description of that calculus is made, collecting some fragmented results on several publications. It is a fundamental tool of study along the thesis. We also present an alternative demonstration of the result of H.Sussmann about coordinates of second kind using the mentioned tools. This simple and comprehensive proof shows that coordinates of second kind are exactly the image of elements of the dual basis of a Hall basis, under the above discussed homomorphism. We obtain explicit expressions for the logarithm of Chen series and the respective coordinates of first kind, by defining several operations on a forest of leaf-labelled trees. It is the same as saying that we have an explicit formula for the functional coefficients of the Lie brackets on a continuous Baker-Campbell-Hausdorff-Dynkin formula when a Hall basis is used. We apply those formulas to relate some noncommutative symmetric functions, and we also connect the monodromy map of a time-periodic nonlinear vector field with a truncation of the Chen logarithm. On the second topic, we study any system of two bodies rolling one over the other without twisting or slipping. By using the Chen logarithm expressions, the monodromy map of a flow and Lyapunov functions, we construct time-variant controls that turn the origin of a control system linear in control into a locally asymptotically stable equilibrium point. Stabilizers for control systems whose vector fields generate a nilpotent Lie algebra with degree of nilpotency · 3 are also given. Some examples are presented and Maple°c were implemented. The third topic, on appendix, concerns the construction of efficient algorithms for Digital Arithmetic, potentially for the implementation in microprocessors. The algorithms are intended for the computation of several functions as the division, square root, sines, cosines, exponential, logarithm, etc. By using redundant number representations and methods of Lyapunov stability for discrete dynamical systems, we obtain several algorithms (that can be glued together into an algorithm for parallel execution) having the same core and selection scheme in each iteration. We also prove their domains of convergence and discuss possible extensions. The last topic, also on appendix, studies the set of solutions of a class of nonlinear Fredholm integral equations with general delay. The delay is of functional character modelled by a continuous lag function. We ensure existence and uniqueness of a continuous (positive) solution of such equation. Moreover, under additional conditions, it is obtained the Fr´echet differentiability of the solution with respect to the lag function.
41
Jo, Jang Hyen. "On the lyapunov-based approach to robustness bounds." Thesis, 1991. http://hdl.handle.net/1957/37156.
Full textAbstract:
The objective of this investigation is the development
of improved techniques for the estimation of robustness for
dynamic systems with structured uncertainties, a problem
which was approached by application of the Lyapunov direct
method. This thesis considers the sign properties of the
Lyapunov function derivative integrated along finite intervals
of time, in place of the traditional method of the
sign properties of the derivative itself.
This proposed approach relaxes the sufficient conditions
of stability, and is used to generate techniques for
the robust design of control systems with structured perturbations.
The need for such techniques has been demonstrated
by recent research interest in the area of robust
control design.
The system considered is assumed to be nominally linear,
with time-variant, nonlinear bounded perturbations.
Application of the proposed technique warrants that estimates
of robustness will either match or constitute an improvement
upon those obtained by application of the traditional
Lyapunov approach. The application of numerical
procedures are used to demonstrate improvements in estimations
of robustness for two-, three- and four-dimensional
dynamic systems with one or more structured perturbations.
The proposed numerical approaches obtain improved bounds,
which are considered in the sense of their engineering aspects.
To increase the accuracy of the numerical procedures,
symbolic algebraic calculations are utilized.Graduation date: 1991
42
McBride, Dean Christian Tait. "An investigation of techniques for nonlinear state observation." Thesis, 2016. http://hdl.handle.net/10539/22656.
Full textAbstract:
A dissertation submitted to the Faculty of Engineering and the Built Environment,
University of the Witwatersrand, in fulfilment of the requirements for the degree of
Master of Science in Engineering.
Johannesburg, 2016An investigation and analysis of a collection of different techniques, for estimating the states of nonlinear systems, was undertaken. It was found that most of the existing literature on the topic could be organized into several groups of nonlinear observer design techniques, of which each group follows a specific concept and slight variations thereof. From out of this investigation it was discovered that a variation of the adaptive observer could be successfully applied to numerous nonlinear systems, given only limited output information. This particular technique formed the foundation on which a design procedure was developed in order to asymptotically estimate the states of nonlinear systems of a certain form, using only partial state information available. Lyapunov stability theory was used to prove the validity of this technique, given that certain conditions and assumptions are satisfied. A heuristic procedure was then developed to get a linearized model of the error transient behaviour that could form the upper bounds of the transient times of the observer. The technique above, characterized by a design algorithm, was then applied to three well-known nonlinear systems; namely the Lorenz attractor, the Rössler attractor, and the Van Der Pol oscillator. The results, illustrated through numerical simulation, clearly indicate that the technique developed is successful, provided all assumptions and conditions are satisfied.
MT2017
43
Alam, Arshad. "Robustness estimation via integral liapunov functions." Thesis, 1992. http://hdl.handle.net/1957/36338.
Full textAbstract:
An investigation focusing on methods of estimation
of robustness of nominally linear dynamic systems with
unstructured uncertainties was performed.
The algorithm proposed involves the consideration
of an associated system, selection, and subsequent
development, of Liapunov function candidate and integration
of their derivatives along the solution trajectory.
A nominally linear multi-dimensional dynamic
system is considered with unstructured, nonlinear, time-varying
and bounded perturbations. The examples illustrate
the success of the method: better estimates of the bounds,
than those which results from traditional approaches were
obtained.
Robustness of linear, time-invariant systems
subject to nonlinear, time-varying perturbations has been a
matter of considerable research interest recently. Design of
conventional state-feedback controllers requires knowledge of
the bounds for disturbances. The knowledge of disturbance
bounds is also important in adaptive control and control of
nonlinear & uncertain systems. Numerous applications can be
found in the fields of automation, aircraft control,
manipulator trajectory control, etc.
The technique for the determination of robust
stability bounds proposed in this paper can be utilized
effectively in computerized robust control system design.Graduation date: 1992
44
Zarei-nia, Kurosh. "Haptic-enabled teleoperation of hydraulic manipulators: theory and application." 2012. http://hdl.handle.net/1993/5113.
Full textAbstract:
Hydraulic manipulators commonly interact with environments that are highly unstructured, and thus rely on the intelligence of human operators to provide proper commands. Typically, operators use visual information, directly or through cameras, to perform a task. Providing haptic or touch sensation about the task environment to the operator, enhances her/his ability to perform telemanipulation. The focus of this thesis is on haptic teleoperation of hydraulic manipulators. The application is directed at live transmission line maintenance tasks.
In this thesis, both unilateral and bilateral haptic teleoperation of hydraulic manipulators are investigated. On the unilateral telemanipulation front, position error is shown to be an important issue in performing repetitive tasks. The most important sources of inaccuracy in position are sensors, robot controller performance, and the operator. To reduce the human operator’s errors, the concept of virtual fixtures is adopted in this research. It is shown that virtual fixtures can help operators perform routine tasks related to live line maintenance.
Stability and telepresence are the main issues in reference to bilateral control. Three stable bilateral control schemes are designed for haptic teleoperation of hydraulic actuators considering nonlinear dynamics of hydraulic actuation, haptic device, and the operator. For each control scheme, stability of the entire control system is proven theoretically by constructing a proper Lyapunov function. Due to the discontinuity originating from a sign function in the control laws, the proposed control systems are non-smooth. Thus, the existence, continuation, and uniqueness of Filippov’s solution to the system are first proven for each control system. Next, the extensions of Lyapunov’s stability theory to non-smooth systems and LaSalle’s invariant set theorems are employed to prove the asymptotic stability of the control systems. In terms of telepresence, two types of haptic sensation are provided to the operator: (i) haptic based on the reflected interaction force, and (ii) haptic based on the position error. Performances of all proposed controllers are validated by experimental results on a hydraulic actuator controlled by a haptic device. It is shown that besides stability, the hydraulic actuator performs well in terms of position tracking while the haptic device provides telepresence for the operator.
45
"Parallel Optimization of Polynomials for Large-scale Problems in Stability and Control." Doctoral diss., 2016. http://hdl.handle.net/2286/R.I.38411.
Full textAbstract:
abstract: In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems - in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) - whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers - machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers.
We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to efficiently utilize hundreds and potentially thousands of processors, and analyze systems with 100+ dimensional state-space. Furthermore, we extend our algorithms to analyze robust stability over more complicated geometries such as hypercubes and arbitrary convex polytopes. Our algorithms can be readily extended to address a wide variety of problems in control such as Hinfinity synthesis for systems with parametric uncertainty and computing control Lyapunov functions.Dissertation/Thesis
Doctoral Dissertation Mechanical Engineering 2016
46
Podder, Chandra Nath. "Mathematics of HSV-2 Dynamics." 2010. http://hdl.handle.net/1993/4082.
Full textAbstract:
The thesis is based on using dynamical systems theories and techniques to study the qualitative dynamics of herpes simplex virus type 2 (HSV-2), a sexually-transmitted disease of major public health significance.
A deterministic model for the interaction of the virus with the immune system in the body of an infected individual (in vivo) is designed first
of all. It is shown, using Lyapunov function and LaSalle's Invariance Principle, that
the virus-free equilibrium of the model is globally-asymptotically stable whenever a
certain biological threshold, known as the reproduction number, is less than unity. Furthermore, the model has at least one virus-present equilibrium when the threshold quantity exceeds unity. Using persistence theory, it is shown that the virus will always be present in vivo whenever the reproduction threshold exceeds unity. The analyses (theoretical and numerical) of this model show that a future HSV-2 vaccine that enhances cell-mediated immune response will be effective in
curtailling HSV-2 burden in vivo.
A new single-group model for the spread of HSV-2 in
a homogenously-mixed sexually-active population is also designed. The disease-free equilibrium of the model is globally-asymptotically stable when its associated reproduction number is less
than unity. The model has a unique endemic equilibrium, which is shown to be
globally-stable for a special case, when the reproduction number exceeds unity.
The model is extended to incorporate an imperfect vaccine with some therapeutic benefits.
Using centre manifold theory, it is shown that the resulting vaccination model undergoes a vaccine-induced backward bifurcation (the epidemiological
importance of the phenomenon of backward bifurcation is that the
classical requirement of having the reproduction threshold less than unity is, although necessary, no longer sufficient for disease elimination. In such a case, disease elimination depends upon the initial sizes of the
sub-populations of the model). Furthermore, it is shown that the use of such an
imperfect vaccine could lead to a positive or detrimental population-level impact (depending on the sign of a certain threshold quantity).
The model is extended to incorporate the effect of variability in HSV-2 susceptibility due to gender differences. The resulting two-group (sex-structured) model is shown to have essentially the
same qualitative dynamics as the single-group model. Furthermore, it is shown that adding periodicity to the corresponding autonomous two-group model does not alter the dynamics of the autonomous two-group model (with respect to the elimination of the disease). The model is used to evaluate the impact of various anti-HSV control strategies.
Finally, the two-group model is further extended to address the effect of risk structure (i.e., risk of acquiring or transmitting HSV-2). Unlike the two-group model described above, it
is shown that the risk-structured model undergoes backward
bifurcation under certain conditions (the backward bifurcation property can be removed if the susceptible population is not stratified according to the risk of acquiring infection). Thus, one of the main findings of this thesis is that risk structure can induce the phenomenon of backward bifurcation in the transmission dynamics of HSV-2 in a population.
47
Melesse, Dessalegn Yizengaw. "Mathematical Analysis of an SEIRS Model with Multiple Latent and Infectious Stages in Periodic and Non-periodic Environments." 2010. http://hdl.handle.net/1993/4086.
Full textAbstract:
The thesis focuses on the qualitative analysis of a general class of SEIRS models in periodic and non-periodic environments. The classical SEIRS model, with standard incidence function, is, first of all, extended to incorporate multiple infectious stages. Using Lyapunov function theory and LaSalle's Invariance Principle, the disease-free equilibrium (DFE) of the resulting SEInRS model is shown to be globally-asymptotically stable whenever the associated reproduction number is less than unity. Furthermore, this model has a unique endemic equilibrium point (EEP), which is shown (using a non-linear Lyapunov function of Goh-Volterra type) to be globally-asymptotically stable for a special case. The SEInRS model is further extended to incorporate arbitrary number of latent stages. A notable feature of the resulting SEmInRS model is that it uses gamma distribution assumptions for the average waiting times in the latent (m) and infectious (n) stages. Like in the case of the SEInRS model, the SEmInRS model also has a globally-asymptotically stable DFE when its associated reproduction threshold is less than unity, and it has a unique EEP (which is globally-stable for a special case) when the threshold exceeds unity. The SEmInRS model is further extended to incorporate the effect of periodicity on the disease transmission dynamics. The resulting non-autonomous SEmInRS model is shown to have a globally-stable disease-free solution when the associated reproduction ratio is less than unity. Furthermore, the non-autonomous model has at least one positive (non-trivial) periodic solution when the reproduction ratio exceeds unity. It is shown (using persistence theory) that, for the non-autonomous model, the disease will always persist in the population whenever the reproduction ratio is greater than unity. One of the main mathematical contributions of this thesis is that it shows that adding multiple latent and infectious stages, gamma distribution assumptions (for the average waiting times in these stages) and periodicity to the classical SEIRS model (with standard incidence) does not alter the main qualitative dynamics (pertaining to the persistence or elimination of the disease from the population) of the SEIRS model.
48
Liu, Jun. "Qualitative Studies of Nonlinear Hybrid Systems." Thesis, 2010. http://hdl.handle.net/10012/5658.
Full textAbstract:
A hybrid system is a dynamical system that exhibits both continuous and discrete dynamic behavior. Hybrid systems arise in a wide variety of important applications in diverse areas, ranging from biology to computer science to air traffic dynamics. The interaction of continuous- and discrete-time dynamics in a hybrid system often leads to very rich dynamical behavior and phenomena that are not encountered in purely continuous- or discrete-time systems. Investigating the dynamical behavior of hybrid systems is of great theoretical and practical importance.
The objectives of this thesis are to develop the qualitative theory of nonlinear hybrid systems with impulses, time-delay, switching modes, and stochastic disturbances, to develop algorithms and perform analysis for hybrid systems with an emphasis on stability and control, and to apply the theory and methods to real-world application problems.
Switched nonlinear systems are formulated as a family of nonlinear differential equations, called subsystems, together with a switching signal that selects the continuous dynamics among the subsystems. Uniform stability is studied emphasizing the situation where both stable and unstable subsystems are present. Uniformity of stability refers to both the initial time and a family of switching signals. Stabilization of nonlinear systems via state-dependent switching signal is investigated. Based on assumptions on a convex linear combination of the nonlinear vector fields, a generalized minimal rule is proposed to generate stabilizing switching signals that are well-defined and do not exhibit chattering or Zeno behavior.
Impulsive switched systems are hybrid systems exhibiting both impulse and switching effects, and are mathematically formulated as a switched nonlinear system coupled with a sequence of nonlinear difference equations that act on the switched system at discrete times. Impulsive switching signals integrate both impulsive and switching laws that specify when and how impulses and switching occur. Invariance principles can be used to investigate asymptotic stability in the absence of a strict Lyapunov function. An invariance principle is established for impulsive switched systems under weak dwell-time signals. Applications of this invariance principle provide several asymptotic stability criteria. Input-to-state stability notions are formulated in terms of two different measures, which not only unify various stability notions under the stability theory in two measures, but also bridge this theory with the existent input/output theories for nonlinear systems. Input-to-state stability results are obtained for impulsive switched systems under generalized dwell-time signals. Hybrid time-delay systems are hybrid systems with dependence on the past states of the systems. Switched delay systems and impulsive switched systems are special classes of hybrid time-delay systems. Both invariance property and input-to-state stability are extended to cover hybrid time-delay systems.
Stochastic hybrid systems are hybrid systems subject to random disturbances, and are formulated using stochastic differential equations. Focused on stochastic hybrid systems with time-delay, a fundamental theory regarding existence and uniqueness of solutions is established. Stabilization schemes for stochastic delay systems using state-dependent switching and stabilizing impulses are proposed, both emphasizing the situation where all the subsystems are unstable. Concerning general stochastic hybrid systems with time-delay, the Razumikhin technique and multiple Lyapunov functions are combined to obtain several Razumikhin-type theorems on both moment and almost sure stability of stochastic hybrid systems with time-delay.
Consensus problems in networked multi-agent systems and global convergence of artificial neural networks are
related to qualitative studies of hybrid systems in the sense that dynamic switching, impulsive effects, communication time-delays, and random disturbances are ubiquitous in networked systems. Consensus protocols are proposed for reaching consensus among networked agents despite switching network topologies, communication time-delays, and measurement noises. Focused on neural networks with discontinuous neuron activation functions and mixed time-delays, sufficient conditions for existence and uniqueness of equilibrium and global convergence and stability are derived using both linear matrix inequalities and M-matrix type conditions.
Numerical examples and simulations are presented throughout this thesis to illustrate the theoretical results.
49
XIAO, XI-JIAN, and 蕭錫堅. "Operators similar to strict contractions and the stability theorem of lyapunov." Thesis, 1991. http://ndltd.ncl.edu.tw/handle/66811803464815443733.
Full text
50
Shuai, Zhisheng. "A graph-theoretic approach to the construction of Lyapunov functions for coupled systems on networks." Phd thesis, 2010. http://hdl.handle.net/10048/1305.
Full textAbstract:
For coupled systems of differential equations on networks, a graph-theoretic approach to the construction of Lyapunov functions is systematically developed in this thesis. Kirchhoffs Matrix-Tree Theorem in graph theory plays
an essential role in the approachs development. The approach is successfully applied to several coupled systems well-known in the literature to demonstrate its applicability and effectiveness.Applied Mathematics