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Beauchamp, Gerson. "Algorithms for singular systems." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/15368.
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Heck, Bonnie S. "On singular perturbation theory for piecewise-linear systems." Diss., Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/15054.
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JADANZA, RICCARDO DANILO. "Morse index and linear stability of relative equilibria in singular mechanical systems." Doctoral thesis, Politecnico di Torino, 2015. http://hdl.handle.net/11583/2599754.
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We have focussed on the study of the linear stability of some particular periodic orbits (called relative equilibria) in planar singular mechanical systems with SO(2)-symmetry, and we have achieved the results using quite advanced mathematical techniques. These involve some homotopy invariants, such as the spectral flow, and some index theory, namely a theorem stating the equality between the Morse index of an orbit seen as a critical point of a Lagrange action functional and the Maslov index of the fundamental solution of the associated Hamiltonian system. Moreover, what we have found meets one of its most important applications in a generalised n-body problem, that is, an n-body problem with a more general potential.
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Bushong, Philip Merton. "A multi-loop guidance scheme using singular perturbation and linear quadratic regulator techniques simultaneously." Diss., This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-07282008-135643/.
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Liu, Jie. "State Estimation for Linear Singular and Nonlinear Dynamical Systems Based on Observable Canonical Forms." Electronic Thesis or Diss., Bourges, INSA Centre Val de Loire, 2024. http://www.theses.fr/2024ISAB0002.
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Cette thèse a pour objectif, d’une part, de concevoir des estimateurs pour les systèmessinguliers linéaires en utilisant la méthode des fonctions de modulation. D’autrepart, elle vise à développer des observateurs pour une classe de systèmes dynamiquesnon linéaires en utilisant la méthode des formes normales d’observateurs. Pour lessystèmes singuliers, les estimateurs conçus sont présentés sous forme de formulesintégrales algébriques, garantissant une convergence non asymptotique. Une caractéristique essentielle des algorithmes d’estimation conçus est que les mesures bruitées des sorties ne sont impliquées que dans des termes intégraux, conférant ainsi aux estimateurs une robustesse face aux bruits perturbateurs. Pour les systèmes non linéaires, l’idée principale de conception consiste à transformer les systèmes proposés en une forme simplifiée qui supporte les observateurs existants tels que l’observateur à grandgain et l’observateur en mode glissant. Cette forme simple est appelée forme canoniqueobservable dépendant de la sortie auxiliaire.Pour les systèmes singuliers linéaires, nous transformons le système considéré enune forme similaire à la forme canonique observable de Brunovsky en injectant lesdérivées des entrées et des sorties. Tout d’abord, pour les systèmes singuliers linéairesmono-entrée mono-sortie, la condition d’observabilité est proposée. Des formules algébriques avec une fenêtre d’intégration glissante sont obtenues pour les variables dans différentes situations sans connaître la condition initiale du système. Ensuite, pour les systèmes singuliers linéaires à multiples entrées et sorties, une méthode innovante d’estimation non asymptotique et robuste basée sur la forme canonique observable à l’aide d’un ensemble de systèmes dynamiques de modulation auxiliaires est introduite. Ces derniers systèmes auxiliaires sont donnés par la forme canonique observable contrôlable avec des conditions initiales nulles. En introduisant un ensemble de systèmes dynamiques de modulation auxiliaires qui fournit un cadre plus général pour générer les fonctions de modulation requises, des formules intégrales algébriques sont obtenues à la fois pour les variables d’état et les dérivées de sortie. De plus, l’efficacité et la robustesse des estimateurs proposés sont vérifiées par des simulations numériques dans cette thèse.Pour les systèmes dynamiques non linéaires, nous proposons une famille de systèmesdynamiques non linéaires à multiples sorties "prêts à porter" qui peuvent êtretransformés en formes normales d’observateurs dépendant de la sortie auxiliaire, permettant ainsi le support de l’observateur en mode glissant bien connu. Pour cela, aumoyen de la méthode d’extension de dynamique et d’un ensemble des changementsde coordonnées (calculs algébriques intégraux de base), les termes non linéairessont annulés par une dynamique auxiliaire ou remplacés par des fonctions non linéairesdes multiples sorties. Il convient de mentionner que cette procédure est menée à biende manière compréhensible sans recourir aux outils de la géométrie différentielle, cequi est convivial pour ceux qui ne sont pas familiers avec les calculs des crochets deLie. De plus, l’efficacité et la robustesse des observateurs proposés sont vérifiées pardes simulations numériques dans cette thèse. Deuxièmement, une classe plus large desystèmes dynamiques non linéaires à multiples entrées et sorties "prêts à porter" estfournie pour étendre et développer davantage les systèmes proposés dans le premiercas. De manière similaire, au moyen de la dynamique auxiliaire correspondante etd’un ensemble des changements de coordonnées, les systèmes fournis sont convertisen formes normales non linéaires ciblées dépendant à la fois des multiples sorties etdes variables auxiliaires. Naturellement, cette procédure est également réalisée sansrecourir aux outils géométriques. Enfin, des conclusions sont présentées avec quelques perspectives<br>This thesis aims, on the one hand, to design estimators for linear singular systems usingthemethod of modulation functions. On the other hand, it aims to develop observersfor a class of nonlinear dynamical systems using the method of canonical formsof observers. For singular systems, the designed estimators are presented in the formof algebraic integral equations, ensuring non-asymptotic convergence. An essentialcharacteristic of the designed estimation algorithms is that noisy measurements of theoutputs are only involved in integral terms, thereby imparting robustness to the estimatorsagainst perturbing noises. For nonlinear systems, the main design idea is totransform the proposed systems into a simplified form that accommodates existingobservers such as the high-gain observer and the sliding-mode observer. This simpleformis called auxiliary output depending observable canonical form.For the linear singular systems, we transform the considered system into a formsimilar to the Brunovsky’s observable canonical form with the injection of the inputs’and outputs’ derivatives. First, for linear singular systems with single input and singleoutput, the observability condition is proposed. The system’s input-output differentialequation is derived based on the Brunovsky’s observable canonical form. Algebraicformulas with a sliding integration window are obtained for the variables in differentsituations without knowing the system’s initial condition. Second, for linear singular systemswith multiple input and multiple output, an innovative nonasymptotic and robust estimation method based on the observable canonical form by means of a set of auxiliary modulating dynamical systems is introduced. The latter auxiliary systems are given by the controllable observable canonical with zero initial conditions. The proposed method is applied to estimate the states and the output’s derivatives for linear singular system in noisy environment. By introducing a set of auxiliary modulating dynamical systems which provides a more general framework for generating the requiredmodulating functions, algebraic integral formulas are obtained both for the state variables and the output’s derivatives. After giving the solutions of the required auxiliary systems, error analysis in discrete noisy case is addressed, where the provided noise error bound can be used to select design parameters.For the nonlinear dynamical systems, we propose a family of "ready to wear" nonlineardynamical systemswith multiple outputs that can be transformed into the outputauxiliarydepending observer normal forms which can support the well-known slidingmode observer. For this, by means of the so-called dynamics extension method anda set of changes of coordinates (basic algebraic integral computations), the nonlinearterms are canceled by auxiliary dynamics or replaced by nonlinear functions of themultiple outputs. It is worth mentioning that this procedure is finished in a comprehensible way without resort to the tools of differential geometry, which is user-friendly for those who are not familiar with the computations of Lie brackets. In addition, the efficiency and robustness of the proposed observers are verified by numerical simulations in this thesis. Second, a larger class of "ready to wear" nonlinear dynamicalsystems with multiple inputs and multiple outputs are provided to further extend anddevelop the systems proposed in the first case. In a similar way, by means of the corresponding auxiliary dynamics and a set of changes of coordinates, the provided systems are converted into targeted nonlinear observable canonical forms depending on both the multiple outputs and auxiliary variables. Naturally, this procedure is still completed without resort to geometrical tools. Finally, conclusions are outlined with some perspectives
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Vera, Miler Jerković. "Primena uopštenih inverza u rešavanju fazi linearnih sistema." Phd thesis, Univerzitet u Novom Sadu, Fakultet tehničkih nauka u Novom Sadu, 2018. https://www.cris.uns.ac.rs/record.jsf?recordId=107117&source=NDLTD&language=en.
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Predmet izučavanja doktorske disertacije jeste postavljanje univerzalne metode za rešavanje fazi linearnih sistema primenom blokovske reprezentacije uopštenih inverza matrice. Pre svega, postavljen je potreban i dovoljan uslov za ekzistenciju rešanja fazi linearnog sistema. Zatim je data tačna algebarska forma rešenja i na kraju je predstavljen efikasan algoritam.<br>Thе subject of research of thesis is setting universal method for solving fuzzy linear systems using a block representation of generalized inversis of a matrix. A necessary and sufficienf condition for the existence solutions of fuzzy linear systems is given. The exact algebraic form of any solutiof fuzzy linear system is established.
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Martínez, Gonzáles Alejandro. "Perturbation Analysis of Eigenvalues for LTI Delay Systems. Regular and Singular Cases." Electronic Thesis or Diss., université Paris-Saclay, 2021. http://www.theses.fr/2021UPASG017.
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Dans ce mémoire, on considère l’analyse des effets induits par les retards sur le comportement des systèmes dynamiques d´écrits par des équations différentielles linéaires à retards incluant des retards discrets dans leur représentation mathématique. Les apports principaux de la thèse concernent la caractérisation du comportement asymptotiques des racines caractéristiques multiples dans deux configurations: un ou deux paramètres (retards). Les résultats proposés et les algorithmes associés permettent de mieux comprendre les mécanismes sous-jacentes (un ou deux retards) et assouplissent les conditions existantes dans la littérature du domaines (deux retards, vus comme paramètres). Pour obtenir de tels critères, l’approche proposée combine le théorème de préparation de Weierstrass avec la méthode du diagramme de Newton. Finalement, ces idées sont également utilisés pour étudier le caractère bien-posé/mal-posé d’un système en boucle fermée en présence d’un contrôleur de type Proportionnel-Dérivé quand la ”dérivé” est approximée en utilisant un opérateur aux différences incluant un retard. Dans ce dernier cas d’étude, les résultats obtenus sont des conditions nécessaires et suffisantes<br>This dissertation is devoted to the analysis of the effects induced by the delays on the behavior of the dynamical systems described by linear delay-differential equations of retarded type including discrete delays in their mathematical represen-tation. The main contributions of the thesis concern the characterization of the asymptotic behavior of multiple characteristic roots with respect to the delays in two configurations: one or two (delay) parameters. The proposed results and related algorithms give a better understanding of the underlying mechanisms (one or two delay parameters) and relax the existing conditions from the open literature (two delays, seen as parameters). To derive such criteria, the proposed approach combines the Weierstrass Preparation Theorem with the Newton Diagram Method. Finally, such ideas are also used to study the ill-posed/well-posed character of a closed-loop system when the derivative action is approximated by a delay-difference operator. In this last case study, the corresponding derived conditions are necessary and sufficient
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Lang, Norman, Jens Saak, and Tatjana Stykel. "Balanced truncation model reduction for linear time-varying systems." Universitätsbibliothek Chemnitz, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-183870.
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A practical procedure based on implicit time integration methods applied to the differential Lyapunov equations arising in the square root balanced truncation method is presented. The application of high order time integrators results in indefinite right-hand sides of the algebraic Lyapunov equations that have to be solved within every time step. Therefore, classical methods exploiting the inherent low-rank structure often observed for practical applications end up in complex data and arithmetic. Avoiding the additional effort treating complex quantities, a symmetric indefinite factorization of both the right-hand side and the solution of the differential Lyapunov equations is applied.
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Tang, Ying. "Stability analysis and Tikhonov approximation for linear singularly perturbed hyperbolic systems." Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAT054/document.
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Les dynamiques des systèmes modélisés par des équations aux dérivées partielles (EDPs) en dimension infinie sont largement liées aux réseaux physiques. La synthèse de la commande et l'analyse de la stabilité de ces systèmes sont étudiées dans cette thèse. Les systèmes singulièrement perturbés, contenant des échelles de temps multiples sont naturels dans les systèmes physiques avec des petits paramètres parasitaires, généralement de petites constantes de temps, les masses, les inductances, les moments d'inertie. La théorie des perturbations singulières a été introduite pour le contrôle à la fin des années $1960$, son assimilation dans la théorie du contrôle s'est rapidement développée et est devenue un outil majeur pour l'analyse et la synthèse de la commande des systèmes. Les perturbations singulières sont une façon de négliger la transition rapide, en la considérant dans une échelle de temps rapide séparée. Ce travail de thèse se concentre sur les systèmes hyperboliques linéaires avec des échelles de temps multiples modélisées par un petit paramètre de perturbation. Tout d'abord, nous étudions une classe de systèmes hyperboliques linéaires singulièrement perturbés. Comme le système contient deux échelles de temps, en mettant le paramètre de la perturbation à zéro, deux sous-systèmes, le système réduit et la couche limite, sont formellement calculés. La stabilité du système complet de lois de conservation implique la stabilité des deux sous-systèmes. En revanche un contre-exemple est utilisé pour illustrer que la stabilité des deux sous-systèmes ne suffit pas à garantir la stabilité du système complet. Cela montre une grande différence avec ce qui est bien connu pour les systèmes linéaires en dimension finie modélisés par des équations aux dérivées ordinaires (EDO). De plus, sous certaines conditions, l'approximation de Tikhonov est obtenue pour tels systèmes par la méthode de Lyapunov. Plus précisément, la solution de la dynamique lente du système complet est approchée par la solution du système réduit lorsque le paramètre de la perturbation est suffisamment petit. Deuxièmement, le théorème de Tikhonov est établi pour les systèmes hyperboliques linéaires singulièrement perturbés de lois d'équilibre où les vitesses de transport et les termes sources sont à la fois dépendant du paramètre de la perturbation ainsi que les conditions aux bords. Sous des hypothèses sur la continuité de ces termes et sous la condition de la stabilité, l'estimation de l'erreur entre la dynamique lente du système complet et le système réduit est obtenue en fonction de l'ordre du paramètre de la perturbation. Troisièmement, nous considérons des systèmes EDO-EDP couplés singulièrement perturbés. La stabilité des deux sous-systèmes implique la stabilité du système complet où le paramètre de la perturbation est introduit dans la dynamique de l'EDP. D'autre part, cela n'est pas valable pour le système où le paramètre de la perturbation est présent dans l'EDO. Le théorème Tikhonov pour ces systèmes EDO-EDP couplés est prouvé par la technique de Lyapunov. Enfin, la synthèse de la commande aux bords est abordée en exploitant la méthode des perturbations singulières. Le système réduit converge en temps fini. La synthèse du contrôle aux bords est mise en œuvre pour deux applications différentes afin d'illustrer les résultats principaux de ce travail<br>Systems modeled by partial differential equations (PDEs) with infinite dimensional dynamics are relevant for a wide range of physical networks. The control and stability analysis of such systems become a challenge area. Singularly perturbed systems, containing multiple time scales, often occur naturally in physical systems due to the presence of small parasitic parameters, typically small time constants, masses, inductances, moments of inertia. Singular perturbation was introduced in control engineering in late $1960$s, its assimilation in control theory has rapidly developed and has become a tool for analysis and design of control systems. Singular perturbation is a way of neglecting the fast transition and considering them in a separate fast time scale. The present thesis is concerned with a class of linear hyperbolic systems with multiple time scales modeled by a small perturbation parameter. Firstly we study a class of singularly perturbed linear hyperbolic systems of conservation laws. Since the system contains two time scales, by setting the perturbation parameter to zero, the two subsystems, namely the reduced subsystem and the boundary-layer subsystem, are formally computed. The stability of the full system implies the stability of both subsystems. However a counterexample is used to illustrate that the stability of the two subsystems is not enough to guarantee the full system's stability. This shows a major difference with what is well known for linear finite dimensional systems. Moreover, under certain conditions, the Tikhonov approximation for such system is achieved by Lyapunov method. Precisely, the solution of the slow dynamics of the full system is approximated by the solution of the reduced subsystem for sufficiently small perturbation parameter. Secondly the Tikhonov theorem is established for singularly perturbed linear hyperbolic systems of balance laws where the transport velocities and source terms are both dependent on the perturbation parameter as well as the boundary conditions. Under the assumptions on the continuity for such terms and under the stability condition, the estimate of the error between the slow dynamics of the full system and the reduced subsystem is the order of the perturbation parameter. Thirdly, we consider singularly perturbed coupled ordinary differential equation ODE-PDE systems. The stability of both subsystems implies that of the full system where the perturbation parameter is introduced into the dynamics of the PDE system. On the other hand, this is not true for system where the perturbation parameter is presented to the ODE. The Tikhonov theorem for such coupled ODE-PDE systems is proved by Lyapunov technique. Finally, the boundary control synthesis is achieved based on singular perturbation method. The reduced subsystem is convergent in finite time. Boundary control design to different applications are used to illustrate the main results of this work
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Jesus, Gildson Queiroz de. "Algoritmos array para filtragem de sistemas lineares." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/18/18153/tde-17122007-111519/.
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Esta dissertação desenvolve filtro de informação, algoritmos array para estimador do erro médio mínimo quadrático para sistemas lineares sujeitos a saltos Markovianos e algoritmos array rápidos para filtragem de sistemas singulares convencionais. Exemplos numéricos serão apresentados para mostrarem as vantagens dos algoritmos array deduzidos. Parte dos resultados obtidos nesta pesquisa serão publicados no seguinte artigo: Terra et al. (2007). Terra, M. H., Ishihara, J. Y. and Jesus, G. Q. (2007). Information filtering and array algorithms for discrete-time Markovian jump linear systems. Proceedings of the American Control Conference ACC07.<br>This dissertation develops information filter and array algorithms for linear minimum mean square error estimator (LMMSE) of discrete-time Markovian jump linear systems (MJLSs) and fast array algorithms for filtering of standard singular systems. Numerical examples to show the advantage of the array algorithms are presented. Some results obtained in this research are published in the following paper: Terra et al. (2007). Terra, M. H., Ishihara, J. Y. and Jesus, G. Q. (2007). Information filtering and array algorithms for discrete-time Markovian jump linear systems. Proceedings of the American Control Conference ACC07.
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Daraghmeh, Adnan [Verfasser]. "Model Order Reduction of Linear Control Systems: Comparison of Balance Truncation and Singular Perturbation Approximation with Application to Optimal Control / Adnan Daraghmeh." Berlin : Freie Universität Berlin, 2016. http://d-nb.info/1108270972/34.
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Manfrim, Amanda Liz Pacífico. "Sistemas lineares singulares sujeitos a saltos Markovianos." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/18/18153/tde-08122010-145056/.
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Esta tese trata das propriedades estruturais e do controle de sistemas lineares singulares sujeitos a saltos Markovianos (SLSSM). Três questões fundamentais são consideradas para esta classe de sistemas. A primeira estabelece condições necessárias para que o sistema seja estocasticamente regular em um período de tempo determinado. A segunda trata da estabilidade exponencial estocástica de SLSSM. Equações de Lyapunov acopladas generalizadas são deduzidas para caracterizar estabilidade deste tipo de sistema. Em virtude da complexidade das soluções numéricas dessas equações, cada equação de Lyapunov do conjunto acoplado está em função de duas variáveis desconhecidas, estamos propondo um algoritmo para resolver este problema. A terceira questão diz respeito à síntese de um regulador para este tipo de sistema singular definida em termos de equações algébricas generalizadas de Riccati acopladas.<br>This thesis deals with the structural features and with the control of singular linear systems with Markovian jump parameters (SLSMJP). Three fundamental questions are considered to this class of systems. The first provides necessary conditions to characterize stochastic regularity in a determined period of time. The second deals with exponential stability of SLSMJP. Coupled generalized Lyapunov Equations are deduced to check the stability of this class of systems. In virtue of the complexity of the numerical solutions of these equations, there exist two unknown variables for each equation of the set of coupled Lyapunov equations, we are proposing an algorithm to solve this problem. The third question is related with the synthesis of a regulator for this class of singular systems defined in terms of coupled algebraic generalized Riccati equations.
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Campos, José Carlos Teles. "Filtragem robusta para sistemas singulares discretos no tempo." Universidade de São Paulo, 2004. http://www.teses.usp.br/teses/disponiveis/18/18133/tde-07102015-150651/.
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Esta tese apresenta novos algoritmos que resolvem problemas de estimativas filtrada, suavizadora e preditora para sistemas singulares no tempo discreto usando apenas argumentos determinísticos. Cada capítulo aborda inicialmente as estimativas para o sistema nominal e em seguida, as versões robustas para o sistema com incertezas limitadas. Os resultados encontrados podem ser aplicados tanto em sistemas invariantes como variantes no tempo discreto, utilizando a mesma estrutura do filtro de Kalman. Nos últimos anos, uma quantidade significativa de trabalhos envolvendo estimativas singulares foi publicada enfocando apenas a estimativa filtrada sob a justificativa de que a estimativa preditora era de significativa complexidade quando modelada pelo método dos mínimos quadrados. Por este motivo, poucos trabalhos, como NIKOUKHAH et al. (1992) e ZHANG et al. (1998), deduziram a estimativa preditora. Este último artigo apresentou também um algoritmo para a estimativa suavizadora, mas usando o modelo de inovação ARMA. No entanto, até onde foi possível identificar, nenhum trabalho até agora resolveu o problema de estimativa robusta, considerando incertezas nos parâmetros, para sistemas singulares. Para a dedução das estimativas singulares robustas, esta tese tomou como base SAYED (2001), que deduz o filtro de Kalman robusto com incertezas limitadas utilizando uma abordagem determinística, o chamado filtro BDU. Os filtros robustos para sistemas singulares apresentados nesta tese, são mais abrangentes que os apresentados em SAYED (2001). Quando particularizados para o espaço de estados sem incertezas, todos os filtros se assemelham ao filtro de Kalman.<br>New algorithms to optimal recursive filtering, smoothed and prediction for general time-invariant or time-variant descriptor systems are proposed in this thesis. The estimation problem is addressed as an optimal deterministic trajectory fitting. This problem is solved using exclusively deterministic arguments for systems with or without uncertainties. Kalman type recursive algorithms for robust filtered, predicted and smoothed estimations are derived. In the last years, many papers have paid attention to the estimation problems of linear singular systems. Unfortunately, all those works were concentrated only on the study of filtering problems, for nominal systems. The predicted and smoothed filters are more involved and were considered only by few works : NIKOUKHAH et al. (1992) and ZHANG et al. (1998) had proposed a unified approach for filtering, prediction and smoothing problems which were derived by using the projection formula and were calculated based on the ARMA innovation model, but they had not considered the uncertainties. In this thesis its applied for descriptor systems a robust procedure for usual state space systems developed by SAYED (2001), called BDU filter. It is obtained a robust descriptor Kalman type recursions for filtered, predicted and smoothed estimates. Considering the nominal state space, all descriptor filters developed in this work collapse to the Kalman filter.
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Dufaud, Thomas. "Contribution to the development of Aitken Restricted Additive Schwarz preconditioning and application to linear systems arising from automatic differentiation of compressible Navier-Stokes solutions with respect to the simulation’s parameters." Thesis, Lyon 1, 2011. http://www.theses.fr/2011LYO10230/document.
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Un préconditionneur à deux niveaux, reposant sur la technique d’accélération d’Aitken d’une suite de q vecteurs solutions de l’interface d’un pro- cessus itératif de Schwarz Additif Restreint, est conçu. Cette nouvelle technique, dénomée ARAS(q), utilise une approximation grossière de la solution sur l’interface. Différentes méthodes sont proposées, aboutissant au développement d’une tech- nique d’approximation par Décomposition en Valeures Singulières de la suite de vecteurs. Des implémentations parallèles des méthodes d’Aitken-Schwarz sont pro- posées et l’étude conduit à l’implémentation d’un code totalement algébrique, sur un ou deux niveaux de parallélisation MPI, écrit dans l’environnement de la biblio- thèque PETSc. Cette implémentation pleinement parallèle et algébrique procure un outil flexible pour la résolution de systèmes linéaires tels que ceux issus de la dif- férentiation automatique des solutions de Navier-Stokes dépendant des paramètres de la simulation<br>A two level preconditioner, based on the Aitken acceleration technique of a sequence of q interface’s solution vectors of the Restricted Additive Schwarz iterative process, is designed. This new technique, called ARAS(q), uses a coarse approximation of the solution on the interface. Different methods are discussed, leading to the development of an approximation technique by Singular Value De- composition of the sequence of vectors. Parallel implementations of Aitken-Schwarz methods are proposed, and the study leads to a fully algebraic one-level and two- level MPI implementation of ARAS(q) written into the PETSc library framework. This fully parallel and algebraic code gives an adaptive tool to solve linear systems such as those arising from automatic differentiation of compressible Navier-Stokes solution with respect to the simulation’s parameters
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Arslan, Çiğdem Paşaoğlu Bilender. "Singüler lineer diferensiyel hamilton sistemler /." Isparta : SDÜ Fen Bilimleri Enstitüsü, 2008. http://tez.sdu.edu.tr/Tezler/TF01171.pdf.
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Wikström, Gunilla. "Computation of Parameters in some Mathematical Models." Doctoral thesis, Umeå University, Computing Science, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-565.
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<p>In computational science it is common to describe dynamic systems by mathematical models in forms of differential or integral equations. These models may contain parameters that have to be computed for the model to be complete. For the special type of ordinary differential equations studied in this thesis, the resulting parameter estimation problem is a separable nonlinear least squares problem with equality constraints. This problem can be solved by iteration, but due to complicated computations of derivatives and the existence of several local minima, so called short-cut methods may be an alternative. These methods are based on simplified versions of the original problem. An algorithm, called the modified Kaufman algorithm, is proposed and it takes the separability into account. Moreover, different kinds of discretizations and formulations of the optimization problem are discussed as well as the effect of ill-conditioning.</p><p>Computation of parameters often includes as a part solution of linear system of equations <i>Ax = b</i>. The corresponding pseudoinverse solution depends on the properties of the matrix <i>A</i> and vector <i>b</i>. The singular value decomposition of <i>A</i> can then be used to construct error propagation matrices and by use of these it is possible to investigate how changes in the input data affect the solution <i>x</i>. Theoretical error bounds based on condition numbers indicate the worst case but the use of experimental error analysis makes it possible to also have information about the effect of a more limited amount of perturbations and in that sense be more realistic. It is shown how the effect of perturbations can be analyzed by a semi-experimental analysis. The analysis combines the theory of the error propagation matrices with an experimental error analysis based on randomly generated perturbations that takes the structure of <i>A</i> into account</p>
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Maddah, Sumayya Suzy. "Formal reduction of differential systems : Singularly-perturbed linear differential systems and completely integrable Pfaffian systems with normal crossings." Thesis, Limoges, 2015. http://www.theses.fr/2015LIMO0065/document.
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Dans cette thèse, nous nous sommes intéressés à l'analyse locale de systèmes différentiels linéaires singulièrement perturbés et de systèmes de Pfaff complètement intégrables et multivariés à croisements normaux. De tels systèmes ont une vaste littérature et se retrouvent dans de nombreuses applications. Cependant, leur résolution symbolique est toujours à l'étude. Nos approches reposent sur l'état de l'art de la réduction formelle des systèmes linéaires singuliers d'équations différentielles ordinaires univariées (ODS). Dans le cas des systèmes différentiels linéaires singulièrement perturbés, les complications surviennent essentiellement à cause du phénomène des points tournants. Nous généralisons les notions et les algorithmes introduits pour le traitement des ODS afin de construire des solutions formelles. Les algorithmes sous-jacents sont également autonomes (par exemple la réduction de rang, la classification de la singularité, le calcul de l'indice de restriction). Dans le cas des systèmes de Pfaff, les complications proviennent de l'interdépendance des multiples sous-systèmes et de leur nature multivariée. Néanmoins, nous montrons que les invariants formels de ces systèmes peuvent être récupérés à partir d'un ODS associé, ce qui limite donc le calcul à des corps univariés. De plus, nous donnons un algorithme de réduction de rang et nous discutons des obstacles rencontrés. Outre ces deux systèmes, nous parlons des singularités apparentes des systèmes différentiels univariés dont les coefficients sont des fonctions rationnelles et du problème des valeurs propres perturbées. Les techniques développées au sein de cette thèse facilitent les généralisations d'autres algorithmes disponibles pour les systèmes différentiels univariés aux cas des systèmes bivariés ou multivariés, et aussi aux systèmes d''equations fonctionnelles<br>In this thesis, we are interested in the local analysis of singularly-perturbed linear differential systems and completely integrable Pfaffian systems in several variables. Such systems have a vast literature and arise profoundly in applications. However, their symbolic resolution is still open to investigation. Our approaches rely on the state of art of formal reduction of singular linear systems of ordinary differential equations (ODS) over univariate fields. In the case of singularly-perturbed linear differential systems, the complications arise mainly from the phenomenon of turning points. We extend notions introduced for the treatment of ODS to such systems and generalize corresponding algorithms to construct formal solutions in a neighborhood of a singularity. The underlying components of the formal reduction proposed are stand-alone algorithms as well and serve different purposes (e.g. rank reduction, classification of singularities, computing restraining index). In the case of Pfaffian systems, the complications arise from the interdependence of the multiple components which constitute the former and the multivariate nature of the field within which reduction occurs. However, we show that the formal invariants of such systems can be retrieved from an associated ODS, which limits computations to univariate fields. Furthermore, we complement our work with a rank reduction algorithm and discuss the obstacles encountered. The techniques developed herein paves the way for further generalizations of algorithms available for univariate differential systems to bivariate and multivariate ones, for different types of systems of functional equations
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Zerrougui, Mohamed. "Observation et commande des systèmes singuliers non linéaires." Phd thesis, Université Henri Poincaré - Nancy I, 2011. http://tel.archives-ouvertes.fr/tel-00705339.
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Les travaux présentés dans cette thèse ont été effectués au Centre de Recherche en Automatique de Nancy (CRAN). Ils portent sur l'observation et la commande des systèmes singuliers non linéaires. Dans un premier temps nous nous sommes intéressés à la synthèse d'observateur et au filtrage H infini des systèmes singuliers bilinéaires. Dans un deuxième temps, nous avons étudié la synthèse d'observateur pour les systèmes singuliers non linéaires Lipschitziens. La dernière partie de ce travail concerne la stabilisation et la commande basée observateurs des systèmes singuliers non linéaires. L'objectif de ce travail a été de proposer des résultats facilement implémentables et de couvrir une large classe de systèmes non linéaires. La contribution principale de ce mémoire a été de proposer des observateurs H infini pour les systèmes singuliers non linéaires, en utilisant le non biais de l'erreur d'estimation. Les paramètres de ces observateurs sont obtenus par la résolution des inégalités matricielles linéaires (LMIs). Le deuxième apport concerne la synthèse de commande stabilisante et l'utilisation d'un des observateurs proposés dans cette thèse pour la synthèse d'une commande basée observateur pour les systèmes singuliers non linéaires. Cette dernière est réalisée grâce à la réécriture des fonctions non linéaires sous des formes adéquates à l'application de la commande des systèmes.
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N'Doye, Ibrahima. "Généralisation du lemme de Gronwall-Bellman pour la stabilisation des systèmes fractionnaires." Phd thesis, Université Henri Poincaré - Nancy I, 2011. http://tel.archives-ouvertes.fr/tel-00584402.
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Dans ce mémoire, nous avons proposé une méthode basée sur l'utilisation de la généralisation du lemme de Gronwall-Bellman pour garantir des conditions suffisantes de stabilisation asymptotique pour une classe de systèmes non linéaires fractionnaires. Nous avons étendu ces résultats dans la stabilisation asymptotique des systèmes non linéaires singuliers fractionnaires et proposé des conditions suffisantes de stabilité asymptotique de l'erreur d'observation dans le cas de l'étude des observateurs pour les systèmes non linéaires fractionnaires et singuliers fractionnaires. Pour les systèmes non linéaires à dérivée d'ordre entier, nous avons proposé par l'application de la généralisation du lemme de Gronwall-Bellman des conditions suffisantes pour : - la stabilisation exponentielle par retour d'état statique et par retour de sortie statique, - la stabilisation exponentielle robuste en présence d'incertitudes paramétriques, - la commande basée sur un observateur. Nous avons étudié la stabilisation des systèmes linéaires fractionnaires avec les lois de commande suivantes~: retour d'état statique, retour de sortie statique et retour de sortie basé sur un observateur. Puis, nous avons proposé des conditions suffisantes de stabilisation lorsque le système linéaire fractionnaire est affecté par des incertitudes non linéaires paramétriques. Enfin, nous avons traité la synthèse d'un observateur pour ces systèmes. Les résultats proposés pour les systèmes linéaires fractionnaires ont été étendus au cas où ces systèmes fractionnaires sont singuliers. La technique de stabilisation basée sur l'utilisation de la généralisation du lemme de Gronwall-Bellman est étendue aux systèmes non linéaires fractionnaires et aux systèmes non linéaires singuliers fractionnaires. Des conditions suffisantes de stabilisation asymptotique, de stabilisation asymptotique robuste et de commande basée sur un observateur ont été obtenues pour les classes de systèmes non linéaires fractionnaires et non linéaires singuliers fractionnaires. Par ailleurs, une méthode de synthèse d'observateurs pour ces systèmes non linéaires fractionnaires et non linéaires singuliers fractionnaires est proposée. Cette approche est basée sur la résolution d'un système d'équations de Sylvester. L'avantage de cette méthode est que, d'une part, l'erreur d'observation ne dépend pas explicitement de l'état et de la commande du système et, d'autre part, qu'elle unifie la synthèse d'observateurs de différents ordres (observateurs d'ordre réduit, d'ordre plein et d'ordre minimal).
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Pires, Leonardo. "Rate of convergence of attractors for abstract semilinear problems." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-27102016-090449/.
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In this work we study rate of convergence of attractors for parabolic equations. We consider various types of problems where the diffusion coefficient has varied profiles: large diffusion, localized large diffusion and large diffusion except in the neighborhood of a point where it becomes small. In all cases we obtain a singular perturbation where a rate of convergence of attractors is obtained.<br>Neste trabalho estudamos taxa de convergência de atratores para equações parabólicas. Consideramos vários tipos de problemas onde o coeficiente de difusão apresenta perfís variados: difusão grande, difusão grande localizada e difusão grande exceto na vizinhança de um ponto onde ela torna-se pequena. Em todos os casos consideramos perturbações singulares e uma taxa de convergência para os atratores é obtida.
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Bacha, Inès. "Traitement symbolique des systèmes d'équations différentielles non linéaires au voisinage des singularités." Université Joseph Fourier (Grenoble), 1997. http://www.theses.fr/1997GRE10078.
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Cette these se rattache a l'etude locale des equations differentielles, elle est composee de trois parties dependantes. Dans la premiere partie, nous presentons differentes theories telles que les formes normales, les transformations quasi-monomiales ainsi que celle du polygone de newton afin de mettre en place un algorithme pour simplifier les systemes planaires d'equations differentielles au voisinage des singularites isolees. Cet algorithme se base essentiellement sur les travaux d'a. Bruno sur les solutions locales des systemes d'equations differentielles. Quelques exemples d'application sont donnes afin d'illustrer ce travail. Dans la deuxieme partie, les differentes theories precedentes ainsi que l'etude des courbes algebriques nous permettent d'etendre cet algorithme dans l'espace. Dans la partie finale, nous proposons une methode de reduction de l'ordre des systemes differentiels en dimension n.
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N'Doye, Ibrahima. "Généralisation du lemme de Gronwall-Bellman pour la stabilisation des systèmes fractionnaires." Electronic Thesis or Diss., Nancy 1, 2011. http://www.theses.fr/2011NAN10007.
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Dans ce mémoire, nous avons proposé une méthode basée sur l'utilisation de la généralisation du lemme de Gronwall-Bellman pour garantir des conditions suffisantes de stabilisation asymptotique pour une classe de systèmes non linéaires fractionnaires. Nous avons étendu ces résultats dans la stabilisation asymptotique des systèmes non linéaires singuliers fractionnaires et proposé des conditions suffisantes de stabilité asymptotique de l'erreur d'observation dans le cas de l'étude des observateurs pour les systèmes non linéaires fractionnaires et singuliers fractionnaires.Pour les systèmes non linéaires à dérivée d'ordre entier, nous avons proposé par l'application de la généralisation du lemme de Gronwall-Bellman des conditions suffisantes pour :- la stabilisation exponentielle par retour d'état statique et par retour de sortie statique,- la stabilisation exponentielle robuste en présence d'incertitudes paramétriques,- la commande basée sur un observateur.Nous avons étudié la stabilisation des systèmes linéaires fractionnaires avec les lois de commande suivantes~: retour d'état statique, retour de sortie statique et retour de sortie basé sur un observateur. Puis, nous avons proposé des conditions suffisantes de stabilisation lorsque le système linéaire fractionnaire est affecté par des incertitudes non linéaires paramétriques. Enfin, nous avons traité la synthèse d'un observateur pour ces systèmes. Les résultats proposés pour les systèmes linéaires fractionnaires ont été étendus au cas où ces systèmes fractionnaires sont singuliers.La technique de stabilisation basée sur l'utilisation de la généralisation du lemme de Gronwall-Bellman est étendue aux systèmes non linéaires fractionnaires et aux systèmes non linéaires singuliers fractionnaires. Des conditions suffisantes de stabilisation asymptotique, de stabilisation asymptotique robuste et de commande basée sur un observateur ont été obtenues pour les classes de systèmes non linéaires fractionnaires et non linéaires singuliers fractionnaires.Par ailleurs, une méthode de synthèse d'observateurs pour ces systèmes non linéaires fractionnaires et non linéaires singuliers fractionnaires est proposée. Cette approche est basée sur la résolution d'un système d'équations de Sylvester. L'avantage de cette méthode est que, d'une part, l'erreur d'observation ne dépend pas explicitement de l'état et de la commande du système et, d'autre part, qu'elle unifie la synthèse d'observateurs de différents ordres (observateurs d'ordre réduit, d'ordre plein et d'ordre minimal)<br>In this dissertation, we proposed sufficient conditions for the asymptotical stabilization of a class of nonlinear fractional-order systems based on the generalization of Gronwall-Bellman lemma. We extended these results for the asymptotical stabilization of nonlinear singular fractional-order systems and proposed sufficient conditions for the existence and asymptotic stability of the observation error for the nonlinear fractional-order systems and nonlinear singular fractional-order systems.For the nonlinear integer-order systems, the proposed generalization of Gronwall-Bellman lemma allowed us to obtain sufficient conditions for :- the static state feedback and the static output feedback exponential stabilizations,- the robust exponential stabilization with regards to parameter uncertainties,- the observer-based control.We treated three cases for the asymptotical stabilization of linear fractional-order systems : the static state feedback, the static output feedback and the observer-based output feedback. Then, we proposed sufficient conditions for the asymptotical stabilization of linear fractional-order systems with nonlinear uncertain parameters. Finally, we treated the observer design for the linear and nonlinear fractional-order systems and for the linear and nonlinear singular fractional-order systems.The stabilization technique based on the generalization of Gronwall-Bellman lemma is extended to nonlinear fractional-order systems and nonlinear singular fractional-order systems. Sufficient conditions for the asymptotical stabilization, the robust asymptotical stabilization and the observer-based control of a class of nonlinear fractional-order systems and nonlinear singular fractional-order systems were obtained.Furthermore, the observer design for the nonlinear fractional-order systems and nonlinear singular fractional-order systems is proposed. This approach is based on a parameterization of the solutions of generalized Sylvester equations. The conditions for the existence of these observers are given and sufficient conditions for their stability are derived using linear matrix inequalities (LMIs) formulation and the generalization of Gronwall-Bellman lemma. The advantage of this method is that, firstly, the observation error does not depend explicitly on the state and control system and, secondly, this method unifies the design of full, reduced and minimal orders observers
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Zerrougui, Mohamed. "Observation et commande des systèmes singuliers non linéaires." Electronic Thesis or Diss., Nancy 1, 2011. http://www.theses.fr/2011NAN10143.
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Les travaux présentés dans cette thèse ont été effectués au Centre de Recherche en Automatique de Nancy (CRAN). Ils portent sur l'observation et la commande des systèmes singuliers non linéaires. Dans un premier temps nous nous sommes intéressés à la synthèse d'observateur et au filtrage H infini des systèmes singuliers bilinéaires. Dans un deuxième temps, nous avons étudié la synthèse d'observateur pour les systèmes singuliers non linéaires Lipschitziens. La dernière partie de ce travail concerne la stabilisation et la commande basée observateurs des systèmes singuliers non linéaires. L'objectif de ce travail a été de proposer des résultats facilement implémentables et de couvrir une large classe de systèmes non linéaires. La contribution principale de ce mémoire a été de proposer des observateurs H infini pour les systèmes singuliers non linéaires, en utilisant le non biais de l'erreur d'estimation. Les paramètres de ces observateurs sont obtenus par la résolution des inégalités matricielles linéaires (LMIs). Le deuxième apport concerne la synthèse de commande stabilisante et l'utilisation d'un des observateurs proposés dans cette thèse pour la synthèse d'une commande basée observateur pour les systèmes singuliers non linéaires. Cette dernière est réalisée grâce à la réécriture des fonctions non linéaires sous des formes adéquates à l'application de la commande des systèmes<br>This thesis work is realized in the Research Center in Automatic Control of Nancy (CRAN). It concerns the observation and control of nonlinear singular systems. Firstly, we were interested in the observer design and H infinity filtering for singular bilinear systems. In a second step, we studied the observers design for Lipschitz nonlinear singular systems. The last part of this work relates to the stabilization and observer based controller for a classe of singular nonlinear systems. The objective is to develop a simple and straightforward results which covers a large class of nonlinear systems. The main contribution of this thesis is in the H infinity observers design for nonlinear singular systems. It is based on the parametrization of the solution of the constrained generalized Sylvester equation. The second contribution relates to the design of stabilizing control and using the proposed observer to design an obsever based controller for nonlinear singular systems. Solutions of these problems are obtained by using Linear Matrix Inequalities (LMI) Formulation
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Stolovitch, Laurent. "Classification analytique de champs de vecteurs." Université Joseph Fourier (Grenoble), 1994. http://www.theses.fr/1994GRE10243.
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Cette these a pour objet l'etude des champs de vecteurs analytiques au voisinage d'un point singulier en dimension quelconque. Elle est composee de deux articles. Le premier montre l'existence de varietes analytiques invariantes d'un champ de vecteurs sous des hypotheses de petits diviseurs diophantiens et de resonnances positives. Dans le cas de la dimension 2, nous retrouvons les resultats de dulac. Le deuxieme etudie les champs de vecteurs 1-resonnant. Nous y etudions la linearisation de systemes non-lineaires a singularite irreguliere. Nous montrons l'existence de transformations analytiques dans des domaines sectoriels conjuguant un champ de vecteurs 1-resonnant a sa forme normale, sous certaines hypotheses ; puis, nous donnons une classification analytique des champs ayant une meme forme normale. Nous retrouvons, en dimension 2, celles faites par martinet-ramis sans distinguer les cas du col et du nud-col
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Caleffi, José. "Otimização do método SOR para matrizes p-cíclicas consistentemente ordenadas." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2000. http://hdl.handle.net/10183/126769.
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Estudamos a otimização do método SOR clássico, para a resolução de um sistema linear Ax = b, com A não-singular, a partir dos resultados de Young [55, 57] e Varga [50, 51] para matrizes de blocos p-cíclicas consistentemente ordenadas. Num primeiro nível, a otimização refere-se à escolha do parâmetro de relaxação do SOR que produz a maior velocidade de convergência, e, num segundo nível, à escolha da p-ciclicidade que apresenta o melhor desempenho com os valores ótimos do parâmetro, e damos ênfase ao caso 2-cíclico. Além disso, descrevemos a otimização do parâmetro em três generalizações: a) num relaxamento das condições sobre o espectro da matriz de Jacobi associada a A; b) no método SOR para matrizes singulares; c) num novo método SOR, que substitui a decomposição A = D - L - U, onde D, L e U são a diagonal de A, a parte triangular inferior estrita de A e a parte triangular superior estrita de A, pela A = D - P - Q, onde P pertence a uma classe de matrizes constru ída a partir das matrizes-escada. Descrevemos também a aplicação do caso singular às cadeias de Markov, comentamos a computação paralela aplicada ao SOR, e apresentamos diversas simulações relativas à otimização desse método.<br>We study the optimization of the classic SOR method for solving a linear system Ax = b, where A is a nonsingular p-cyclic consistently ordered block matrix, based on the discoveries of Young [55, 57] and Varga [50, 51]. In a first levei, the optimization refers to the choice of the SOR relaxation parameter, which produces the greatest convergence speed and, in a second levei, to the p-cyclicity that presents the best performance with the optimal parameter values and emphasize the 2- cyclic case. Moreover we describe three SOR generalizations concerning optimization: a) by weakening the conditions on the spectrum of Jacobi matrix associated with A; b) by considering the SOR method for singular matrices; c) by approaching a new SOR, that replaces the splitting A = D - L - U, where O, L and U are the diagonal of A, the strict lower triangular part of A and the strict upper triangular part of A. respectively, by this one A = D - P - Q, where P is a stair matrix or a matrix even more general than a stair matrix. We also describe the application of the singular case to Markov chains, discuss parallel computing applied to SOR method, and present severa! simulations regarding the optimization of that method.
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Arzelier, Denis. "Robustesse en performance et en stabilité des systèmes linéaires incertains : une approche quadratique." Toulouse, INSA, 1992. http://www.theses.fr/1992ISAT0028.
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Cette these a pour sujet la commande robuste des systemes dynamiques lineaires incertains continus, decrits par des equations d'etat. Le probleme de la commande robuste est aborde ici par le biais du concept de stabilisabilite quadratique qui etablit l'existence d'une fonction de lyapunov quadratique pour le systeme. En premier lieu, le probleme des performances est aborde a travers le placement robuste des poles du systeme en boucle fermee dans un secteur du demi-plan complexe gauche. En second lieu, le probleme de la commande robuste par retour de sortie est envisage. Les cas du retour de sortie statique et dynamique ont ete egalement traites. Finalement, une autre classe de modeles lineaires est consideree: les modeles singuliers. Des procedures de stabilisation ont ete developpees sur ces modeles certains et quelques elements de robustesse ont ete introduits sur les modeles singuliers incertains
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Patiño, Diego. "Pilotage des cycles limites dans les systèmes dynamiques hybrides : application aux alimentations électriques statiques." Electronic Thesis or Diss., Vandoeuvre-les-Nancy, INPL, 2009. http://www.theses.fr/2009INPL013N.
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Cette thèse s'intéresse au pilotage des cycles limites pour une classe particulière de systèmes hybrides (SDH): les systèmes commutés cycliques. La thématique des SDH est née du constat d'insuffisance des modèles dynamiques classiques pour décrire les comportements lorsque des aspects évènementiels interviennent. Une classe particulièrement importante de SDH est formée par celle qui présente un régime permanent cyclique. Ces systèmes ont des points de fonctionnement non auto-maintenables: il n'existe pas de commande qui maintienne le système sur ce point. Le maintien n'est assuré qu'en valeur moyenne, en effectuant un cycle dans un voisinage du point par commutation des sous systèmes. L'établissement d'une loi de commutation pour cette classe de systèmes doit répondre aux objectifs de stabilité et de performance dynamique, mais doit également garantir la satisfaction de critères liés à la forme d'onde. A l'heure actuelle, peu de méthodes de commande prennent en compte le caractère cyclique du système. Les travaux de cette thèse ont pour objectif de développer des méthodes génériques et robustes pour piloter cette classe de systèmes. Les algorithmes proposés doivent également pouvoir être implémenté en temps réels. On modélise le système comme un système non - linéaire affine en la commande dont la loi de commande apparait dans le modèle. Ce type de modélisation permet d'envisager deux types de synthèse: l'une à base de commande prédictive et l'autre à base de commande optimale. Ce travail est validé par une partie applicative sur des manipulations dans le CRAN et dans des laboratoires du réseau d'excellence européenne HYCON dans le cadre duquel s'est déroulé cette étude<br>This work deals with limit cycle control for one particular class of hybrid dynamical systems (HDS): The cyclic switched systems. The HDS were born because the traditional dynamical models were not able to describe complex behaviors and most of all, behaviors with discontinuities. From an application point of view, one important class of HDS depicts a cyclic behavior in steady state. The main characteristic of these systems is that the operation point cannot be maintained: It does not exist a control that maintains the system on a desired operation point. However, this point can be obtained in average by turning into its neighborhood. Thus, a cycle is produced by switching among the system modes. A switched control law must satisfy stability and dynamic performance. Moreover, criteria related to the waveform must be verified. Nowadays, few methods take into account the cyclic behavior of the system. In this research, some generic methods are studied. They show good performance for controlling the cyclic switched systems. The proposed algorithms can be implemented in real-time. The approaches are based on an affine non-linear model of the system whose control explicitly appears. Two control methods are considered: i) A predictive control, ii) An optimal control. Since the predictive control is a good choice for tracking, it will be able to maintain the system in a cycle. The optimal control yields solutions that can be applied to the transients. Some experiments with both control methods applied to the power converters are shown. These tests were carried out not only in our laboratory (CRAN), but also in other laboratories as part of the HYCON excellence network
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Patino, Diego. "Pilotage des cycles limites dans les systèmes dynamiques hybrides : application aux alimentations électriques statiques." Phd thesis, Institut National Polytechnique de Lorraine - INPL, 2009. http://tel.archives-ouvertes.fr/tel-00381971.
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Cette thèse s'intéresse au pilotage des cycles limites pour une classe particulière de systèmes hybrides (SDH) : les systèmes commutés cycliques. La thématique des SDH est née du constat d'insuffisance des modèles dynamiques classiques pour décrire les comportements lorsque des aspects évènementiels interviennent. Une classe particulièrement importante de SDH est formée par celle qui présente un régime permanent cyclique. Ces systèmes ont des points de fonctionnement non auto-maintenables : il n'existe pas de commande qui maintienne le système sur ce point. Le maintien n'est assuré qu'en valeur moyenne, en effectuant un cycle dans un voisinage du point par commutation des sous systèmes. L'établissement d'une loi de commutation pour cette classe de systèmes doit répondre aux objectifs de stabilité et de performance dynamique, mais doit également garantir la satisfaction de critères liés à la forme d'onde. A l'heure actuelle, peu de méthodes de commande prennent en compte le caractère cyclique du système. Les travaux de cette thèse ont pour objectif de développer des méthodes génériques et robustes pour piloter cette classe de systèmes. Les algorithmes proposés doivent également pouvoir être implémenté en temps réels. On modélise le système comme un système non - linéaire affine en la commande dont la loi de commande apparait dans le modèle. Ce type de modélisation permet d'envisager deux types de synthèse : l'une à base de commande prédictive et l'autre à base de commande optimale. Ce travail est validé par une partie applicative sur des manipulations dans le CRAN et dans des laboratoires du réseau d'excellence européenne HYCON dans le cadre duquel s'est déroulé cette étude.
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Zhong, Guan-tian, and 鐘冠添. "Generalized H∞ Analysis for Linear Time-Varying Singular Systems." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/66u624.
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碩士<br>國立中山大學<br>電機工程學系研究所<br>106<br>In H∞ control problem, it is usually assumed that the system initial conditions are zero. This thesis extends the results of H∞ control for state-space time-varying systems with nonzero initial conditions to singular time-varying systems, meanwhile redefines the generalized performance index for the considered systems. Necessary and sufficient conditions in the form of linear matrix equality and inequality are derived for singular time-varying systems possessing simultaneously the impulse-free property and the above-mentioned performance measure is less than a pre-specified value. Two kinds of commonly used state feedback controllers are also considered to make the closed-loop singular systems performance specification.
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Zheng, Yang Qi, and 鄭揚旗. "Robust stability analysis for linear systems with singular and nonsingular uncertain parameters." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/29756242265543039017.
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Lin, Ming-Je, and 林銘哲. "Novel Design Methodologies for Quadratic Observers and Trackers of Sampled-Data Linear Singular Systems." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/61766358151901560801.
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碩士<br>國立成功大學<br>電機工程學系碩博士班<br>97<br>This thesis develops novel design methodologies for quadratic observers and trackers of sampled-data linear singular system. At first, some techniques have been utilized to decompose the singular system into an equivalent regular system with a direct transmission term from input to output. Then, a high-gain optimal linear quadratic analogue tracker is proposed based on the equivalent regular system with a direct transmission term from input to output. Subsequently, the prediction-based digital redesign method is utilized to obtain a relatively low-gain and practicably implemental digital tracker. Here, this thesis also derives a method called an alternative digital redesign approach. That this thesis directly discretizes the linear quadratic performance index specified in the continuous-time domain into an equivalent discrete-time performance index for the equivalent regular system with a direct transmission term from input to output. When the state of the continuous-time system with a direct transmission term is not available for measurement, the novel suboptimal analog and its corresponding digital observers are developed for the continuous time and sampled-data linear singular systems, respectively. Several illustrative examples are presented to demonstrate the effectiveness of the proposed design methodology.
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Shu, Chiung-Chao, and 蘇炯超. "Study of Fuzzy Logic Controller Application in Linear Singular System." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/65537897542025982336.
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碩士<br>國立成功大學<br>電機工程學系<br>89<br>In comparing with general system, the control problems of singular systems are more complicated because more operating matrices (E and A) are involved and infinite poles exist in the singular system. In this thesis, we solve these difficulties by decomposing the singular system in simplified structure. This is easy and convenient for system analysis and design. Firstly, because of the equivalent transformation of the system, we can preserves (1) the transfer matrix of the system, (2) the set of system poles and zeros, and (3) characteristic polynomial of the system. So we use the singular value decomposition method to decompose the singular systems. After decomposing the singular system and using transformation, we can get the simplified singular system configuration. We also provide two methods to obtain the state feedback gain. One is the direct method; the other is time scale transformation method. Comparing these two methods it is found that, the second method is easier to give the state feedback gain than the first one. Finally, we use fuzzy logic controller design for singular system with state feedback to achieve output tracking of the system.
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"An algebraic approach to time scale analysis of singularly perturbed linear systems." Laboratory for Information and Decision Systems, Massachusetts Institute of Technology], 1986. http://hdl.handle.net/1721.1/2957.
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Xi-Cheng Lou, Alan S. Willsky, George C. Verghese.<br>Bibliography: p. 41.<br>Supported by the Air Force Office of Scientific Research under grant AFOSR-82-0258 Supported by the Army Research Offcie under grant DAAG-29-84-K-005
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Ali, Mohamed Abdel-Magid Mohamed. "Observers for linear descriptor systems." Rozprawa doktorska, 1994. https://repolis.bg.polsl.pl/dlibra/docmetadata?showContent=true&id=3296.
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Ali, Mohamed Abdel-Magid Mohamed. "Observers for linear descriptor systems." Rozprawa doktorska, 1994. https://delibra.bg.polsl.pl/dlibra/docmetadata?showContent=true&id=3296.
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Chen, Ching-Fa, and 陳清發. "Some Aspects on Robust Stability of Uncertain Linear Singularly Perturbed Systems with Multiple Time Delays." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/83794292303530471484.
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Wei-CinLiao and 廖偉欽. "Modeling of Decentralized Linear Observers and Trackers for the Unknown Sampled-data Interconnected Large-scale Linear Singular System with Time Delay and Closed-loop Decoupling Property." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/47307280640538143658.
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碩士<br>國立成功大學<br>電機工程學系碩博士班<br>98<br>Modeling of decentralized linear observers and trackers for the unknown sampled-data interconnected large-scale linear singular system with time delay and closed-loop decoupling property is proposed in this thesis. Through the off-line observer / Kalman filter identification (OKID), the appropriate (low-) order decentralized linear observers with direct transmission terms from input to output for the unknown sampled-data interconnected large-scale linear singular system with time delay are determined. Then, the high-gain linear quadratic suboptimal analogue observer and tracker are proposed based on the each decentralized equivalent regular system with a direct transmission term from input to output. Subsequently, the prediction-based digital redesign method is utilized to obtain practically implemental digital observer and tracker for the sample-data system. With the high-gain property, the decentralized digital-redesign trackers have the decoupling property for the closed-loop interconnected system. Finally, appropriate weighting of the each decentralized observer can be obtained to improve the performance of observer-based tracker by the evolutionary programming (EP).
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Chen, Yong-Cheng, and 陳泳丞. "An Low-Order Active Fault-Tolerant State-Space Self-Tunerfor Unknown Linear Singular System Using OKID and Modified ARMAX Model-Based System Identification." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/76843605689543347000.
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碩士<br>國立成功大學<br>電機工程學系碩博士班<br>97<br>An low-order active fault-tolerant state-space self-tuner for unknown linear singular system using observer/Kalman filter identification (OKID) and modified autoregressive moving average with exogenous input (ARMAX) model-based system identification is proposed in this thesis. Through OKID, to determination the order and a good initial guess of the modified ARMAX model can be obtained to improve the performance of the identification process. With the modified adjustable ARMAX-based system identification, a corresponding adaptive digital control scheme is proposed for the sampled-data multivariable linear singular system which has unknown system parameter and inaccessible system state. Besides, by modifying the conventional self-tuning control, a fault tolerant control scheme is also developed for the unknown multivariable singular system. For the detection of fault occurrence, a quantitative criterion is developed by comparing the innovation process errors estimated by the Kalman filter estimation algorithm, so that a resetting technique of the weighting matrix is developed by adjusting and resetting the covariance matrices of parameter estimation obtained by the Kalman filter estimation algorithm to improve the parameter estimation for faulty system recovery. The proposed method can effectively cope with partially abrupt and/or gradual system faults and/or input failure with fault detection. An illustrative example is given to demonstrate the effectiveness of the proposed design methodology.
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Chia-HsingChen and 陳家興. "Optimal Tracker and Observer for the Equivalent Model of the Sampled-Data Linear Singular System: Digital Redesign and Iterative Learning Control Approach." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/55683050772296727343.
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博士<br>國立成功大學<br>電機工程學系碩博士班<br>100<br>The research objectives of this dissertation are stated as follows. First, via some existing techniques, the linear singular system can be decomposed into an equivalent regular system with a feedthrough term, from input to output. Second, the high-gain optimal linear quadratic analog tracker and observer for this equivalent model are developed. Third, based on this linear quadratic analog tracker (LQAT) and observer, the prediction-based digital redesign and alternative digital redesign methodologies are carried out, respectively, to derive the digital tracker for the state of the digitally controlled model closely matches the state of theoretically well-design continuous-time model with the same input and initial condition; and the digital observer while, as the states of both digitally controlled model and continuous-time model are unmeasured in turn. Finally, an iterative learning control (ILC) strategy, by combined with the LQAT, for the continuous-time linear time-variant (LTI) regular model with a singular feedthrough term is presented. The tracking performance improvement is achieved through the initial control input obtained by the LQAT, and the initial condition constraint, in typical ILC design, is removed by together with initial state learning law. Some illustrative examples are given to demonstrate the effectiveness of the proposed methodologies.
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Ghous, Hamid. "Building a robust clinical diagnosis support system for childhood cancer using data mining methods." Thesis, 2016. http://hdl.handle.net/10453/90061.
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University of Technology Sydney. Faculty of Engineering and Information Technology.<br>Progress in understanding core pathways and processes of cancer requires thorough analysis of many coding and noncoding regions of the genome. Data mining and knowledge discovery have been applied to datasets across many industries, including bioinformatics. However, data mining faces a major challenge in its application to bioinformatics: the diversity and dimensionality of biomedical data. The term ‘big data’ was applied to the clinical domain by Yoo et al. (2014), specifically referring to single nucleotide polymorphism (SNP) and gene expression data. This research thesis focuses on three different types of data: gene-annotations, gene expression and single nucleotide polymorphisms.
Genetic association studies have led to the discovery of single genetic variants associated with common diseases. However, complex diseases are not caused by a single gene acting alone but are the result of complex linear and non-linear interactions among different types of microarray data. In this scenario, a single gene can have a small effect on disease but cannot be the major cause of the disease. For this reason there is a critical need to implement new approaches which take into account linear and non-linear gene-gene and patient-patient interactions that can eventually help in diagnosis and prognosis of complex diseases. Several computational methods have been developed to deal with gene annotations, gene expressions and SNP data of complex diseases. However, analysis of every gene expression and SNP profile, and finding gene-to-gene relationships, is computationally infeasible because of the high-dimensionality of data. In addition, many computational methods have problems with scaling to large datasets, and with overfitting. Therefore, there is growing interest in applying data mining and machine learning approaches to understand different types of microarray data.
Cancer is the disease that kills the most children in Australia (Torre et al., 2015). Within this thesis, the focus is on childhood Acute Lymphoblastic Leukaemia. Acute Lymphoblastic Leukaemia is the most common childhood malignancy with 24% of all new cancers occurring in children within Australia (Coates et al., 2001). According to the American Cancer Society (2016), a total of 6,590 cases of ALL have been diagnosed across all age groups in USA and the expected deaths are 1,430 in 2016.
The project uses different data mining and visualisation methods applied on different types of biological data: gene annotations, gene expression and SNPs.
This thesis focuses on three main issues in genomic and transcriptomic data studies:
(i) Proposing, implementing and evaluating a novel framework to find functional relationships between genes from gene-annotation data.
(ii) Identifying an optimal dimensionality reduction method to classify between relapsed and non-relapsed ALL patients using gene expression.
(iii) Proposing, implementing and evaluating a novel feature selection approach to identify related metabolic pathways in ALL
This thesis proposes, implements and validates an efficient framework to find functional relationships between genes based on gene-annotation data. The framework is built on a binary matrix and a proximity matrix, where the binary matrix contains information related to genes and their functionality, while the proximity matrix shows similarity between different features. The framework retrieves gene functionality information from Gene Ontology (GO), a publicly available database, and visualises the functional related genes using singular value decomposition (SVD). From a simple list of gene-annotations, this thesis retrieves features (i.e Gene Ontology terms) related to each gene and calculates a similarity measure based on the distance between terms in the GO hierarchy. The distance measures are based on hierarchical structure of Gene Ontology and these distance measures are called similarity measures. In this framework, two different similarity measures are applied:
(i) A hop-based similarity measure where the distance is calculated based on the number of links between two terms.
(ii) An information-content similarity measure where the similarity between terms is based on the probability of GO terms in the gene dataset.
This framework also identifies which method performs better among these two similarity measures at identifying functional relationships between genes. Singular value decomposition method is used for visualisation, having the advantage that multiple types of relationships can be visualised simultaneously (gene-to-gene, term-to-term and gene-to-term)
In this thesis a novel framework is developed for visualizing patient-to-patient relationships using gene expression values. The framework builds on the random forest feature selection method to filter gene expression values and then applies different linear and non-linear machine learning methods to them. The methods used in this framework are Principal Component Analysis (PCA), Kernel Principal Component Analysis (kPCA), Local Linear Embedding (LLE), Stochastic Neighbour Embedding (SNE) and Diffusion Maps. The framework compares these different machine learning methods by tuning different parameters to find the optimal method among them. Area under the curve (AUC) is used to rank the results and SVM is used to classify between relapsed and non-relapsed patients.
The final section of the thesis proposes, implements and validates a framework to find active metabolic pathways in ALL using single nucleotide polymorphism (SNP) profiles. The framework is based on the random forest feature selection method. A collected dataset of ALL patient and healthy controls is constructed and later random forest is applied using different parameters to find highly-ranked SNPs. The credibility of the model is assessed based on the error rate of the confusion matrix and kappa values. Selected high ranked SNPs are used to retrieve metabolic pathways related to ALL from the KEGG metabolic pathways database.
The methodologies and approaches presented in this thesis emphasise the critical role that different types of microarray data play in understanding complex diseases like ALL. The availability of flexible frameworks for the task of disease diagnosis and prognosis, as proposed in this thesis, will play an important role in understanding the genetic basis to common complex diseases.
This thesis contributes to knowledge in two ways:
(i) Providing novel data mining and visualisation frameworks to handle biological data.
(ii) Providing novel visualisations for microarray data to increase understanding of disease.