Relevant bibliographies by topics / Controllability gramian

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Controllability gramian'

Author: Grafiati
Published: 4 June 2021
Last updated: 15 February 2022

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Journal articles on the topic "Controllability gramian"

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Himpe, Christian, and Mario Ohlberger. "Cross-Gramian-Based Combined State and Parameter Reduction for Large-Scale Control Systems." Mathematical Problems in Engineering 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/843869.

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This work introduces the empirical cross-gramian for multiple-input-multiple-output systems. The cross-gramian is a tool for reducing the state space of control systems, by conjoining controllability and observability information into a single matrix and does not require balancing. Its empirical gramian variant extends the applicability of the cross-gramian to nonlinear systems. Furthermore, for parametrized systems, the empirical gramians can also be utilized for sensitivity analysis or parameter identification and thus for parameter reduction. This work also introduces the empirical joint gramian, which is derived from the empirical cross-gramian. The joint gramian allows not only a reduction of the parameter space but also the combined state and parameter space reduction, which is tested on a linear and a nonlinear control system. Controllability- and observability-based combined reduction methods are also presented, which are benchmarked against the joint gramian.
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Dusser, Xavier, and Rabah Rabah. "On exponential stabilizability of linear neutral systems." Mathematical Problems in Engineering 7, no. 1 (2001): 67–86. http://dx.doi.org/10.1155/s1024123x01001533.

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In this paper, we deal with linear neutral functional differential systems. Using an extended state space and an extended control operator, we transform the initial neutral system in an infinite dimensional linear system. We give a sufficient condition for admissibility of the control operatorB, conditions under which operatorBcan be acceptable in order to work with controllability and stabilizability. Necessary and sufficient conditions for exact controllability are provided; in terms of a gramian of controllabilityN(μ). Assuming admissibility and exact controllability, a feedback control law is defined from the inverse of the operatorN(μ)in order to stabilize exponentially the closed loop system. In this case, the semigroup generated by the closed loop system has an arbitrary decay rate.
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Klickstein, Isaac, and Francesco Sorrentino. "The controllability Gramian of lattice graphs." Automatica 114 (April 2020): 108833. http://dx.doi.org/10.1016/j.automatica.2020.108833.

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Zhang, Lifei, Konstantin Avenirovich Neusypin, and Maria Sergeevna Selezneva. "A New Method for Determining the Degree of Controllability of State Variables for the LQR Problem Using the Duality Theorem." Applied Sciences 10, no. 15 (July 29, 2020): 5234. http://dx.doi.org/10.3390/app10155234.

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The control performance of a dynamic system can be checked by the degree of controllability. In this work, we present a new method for determining the degree of observability of state variables for the linear quadratic optimal estimation (LQE) problem. We carried out the calculation of the degree of controllability for the linear quadratic optimal control (LQR) problem using a duality theorem. Compared with the traditional measures of controllability such as determinant, trace, and maximal eigenvalue of the inverse controllability Gramian, the proposed degree of controllability was developed for each state variable and takes into account both the controllability Gramian and the cost function. The new method is convenient to apply to LQR problem. In the numerical simulation, we determined the influence of the model parameters on the degree of controllability. Besides that, we analyzed the degree of controllability, which gives an insight into the relationship between the system model design and the control performance.
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Choo, Younseok, and Dongmin Kim. "SISO Continuous-System Reduction via Impulse Response Gramian by Iterative Formulae." Journal of Dynamic Systems, Measurement, and Control 128, no. 2 (May 22, 2005): 391–93. http://dx.doi.org/10.1115/1.2194075.

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This paper concerns the order reduction of single-input single-output (SISO) linear time-invariant continuous systems based on the impulse response Gramian. From the recursive relationship among the Gramians, a new formula is derived for computing the system matrix in controllability canonical form. The result is applied to the model reduction problem. Reduced models obtained approximate the reduced-order Gramians while preserving some initial time moments and Markov parameters of the original system.
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Alves da Silveira, Otávio Augusto, Jun Sérgio Ono Fonseca, and Ilmar Ferreira Santos. "Actuator topology design using the controllability Gramian." Structural and Multidisciplinary Optimization 51, no. 1 (July 16, 2014): 145–57. http://dx.doi.org/10.1007/s00158-014-1121-z.

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Roy, Sandip, and Mengran Xue. "Controllability-Gramian submatrices for a network consensus model." Systems & Control Letters 136 (February 2020): 104575. http://dx.doi.org/10.1016/j.sysconle.2019.104575.

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Benner, Peter, and Christian Himpe. "Cross-Gramian-based dominant subspaces." Advances in Computational Mathematics 45, no. 5-6 (November 19, 2019): 2533–53. http://dx.doi.org/10.1007/s10444-019-09724-7.

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AbstractA standard approach for model reduction of linear input-output systems is balanced truncation, which is based on the controllability and observability properties of the underlying system. The related dominant subspaces projection model reduction method similarly utilizes these system properties, yet instead of balancing, the associated subspaces are directly conjoined. In this work, we extend the dominant subspace approach by computation via the cross Gramian for linear systems, and describe an a-priori error indicator for this method. Furthermore, efficient computation is discussed alongside numerical examples illustrating these findings.
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Chang, Wen-Jer. "Model-Based Fuzzy Controller Design With Common Observability Gramian Assignment." Journal of Dynamic Systems, Measurement, and Control 123, no. 1 (August 31, 1998): 113–16. http://dx.doi.org/10.1115/1.1344241.

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Almost all robust properties of linear systems can be related directly to properties of the controllability or observability Gramian. A model-based fuzzy controller for a class of uncertain nonlinear systems will be developed in this paper to achieve a common observability Gramian. Design of a model-based fuzzy controller begins by assigning a certain common observability Gramian. The nonlinear systems considered in this paper are represented by Takagi-Sugeno fuzzy models. An application to the inverted pendulum system will be given to demonstrate the effects of the present design method.
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Wang, Yanqing, and Zhiyong Yu. "On the partial controllability of SDEs and the exact controllability of FBSDES." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 68. http://dx.doi.org/10.1051/cocv/2019052.

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A notion of partial controllability (also can be called directional controllability or output controllability) is proposed for linear controlled (forward) stochastic differential equations (SDEs), which characterizes the ability of the state to reach some given random hyperplane. It generalizes the classical notion of exact controllability. For time-invariant system, checkable rank conditions ensuring SDEs’ partial controllability are provided. With some special setting, the partial controllability for SDEs is proved to be equivalent to the exact controllability for linear controlled forward-backward stochastic differential equations (FBSDEs). Moreover, we obtain some equivalent conclusions to partial controllability for SDEs or exact controllability for FBSDEs, including the validity of observability inequalities for the adjoint equations, the solvability of some optimal control problems, the solvability of norm optimal control problems, and the non-singularity of a random version of Gramian matrix.
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Dissertations / Theses on the topic "Controllability gramian"

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Gupta, Rikin. "Incorporating Flight Dynamics and Control Criteria in Aircraft Design Optimization." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/104967.

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The NASA Performance Adaptive Aeroelastic Wing (PAAW) project goals include significant reductions in fuel burn, emissions, and noise via efficient aeroelastic design and improvements in propulsion systems. As modern transport airplane designs become increasingly lightweight and incorporate high aspect-ratio wings, aeroservoelastic effects gain prominence in modeling and design considerations. As a result, the influence of the flight dynamics and controls on the optimal structural and aerodynamic design needs to be captured in the design process. There is an increasing interest in more integrated aircraft multidisciplinary design optimization (MDAO) processes that can bring flight control design into the early stage of an aircraft design cycle. So, in this thesis different flight dynamics modeling methodologies are presented that can be integrated within the MDAO framework. MDAO studies are conducted to maximize the controllability and observability of a UAV type aircraft using curvilinear SpaRibs and straight spars and ribs as the internal structural layout. The impulse residues and controllability Gramians are used as surrogates for the control objectives in the MDAO to maximize the controllability and observability of the aircraft. The optimal control designs are compared with those obtained using weight minimization as the design objective. It is found that using the aforementioned control objectives, the resulting aircraft design is more controllable and can be used to expand the flight envelope by up to 50% as compared to the weight minimized design.
Doctor of Philosophy
Over the last two decades, several attempts have been made towards multidisciplinary design analysis and optimization (MDAO) of flexible wings by integrating flight control laws in the wing design so that the aircraft will have sufficient control authority across different flying conditions. However, most of the studies have been restricted to the wing design only using a predefined control architecture approach, which would be very difficult to implement at the conceptual design stage. There is a need for an approach that would be faster and more practical. Including control surface and control law designs at the conceptual design stage is becoming increasingly important, due to the complexity of both the aircraft control laws and that of the actuation and sensing, and the enhanced wing flexibility of future transport aircraft. A key question that arises is, can one design an aircraft that is more controllable and observable? So, in this thesis, a more fundamental approach, in which the internal structural layout of the aircraft is optimized to design an aircraft that is more controllable, is presented and implemented. The approach uses the fundamentals of linear systems theory for maximizing the controllability and observability of the aircraft using an MDAO framework.
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Gonçalves, Juliano Fagundes. "Otimização topológica para localização de atuadores piezelétricos utilizando gramiano de controlabilidade." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2015. http://hdl.handle.net/10183/114969.

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Este trabalho apresenta a formulação de um problema de otimização topológica para o posicionamento ótimo de atuadores baseado na teoria de controle. A estrutura é composta por dois materiais: um material passivo elástico e um material ativo piezelétrico, ambos lineares. Pretende-se obter um sistema de controle no qual todos os estados sejam controláveis. O processo de otimização topológica busca a distribuição de material piezelétrico que maximize o menor autovalor do Gramiano de controlabilidade garantindo, assim, sua não singularidade e, consequentemente, que o sistema seja completamente controlável. Programação linear sequencial (SLP) é utilizada para a solução do problema de otimização e as sensibilidades para o modelo de elementos finitos são deduzidas para a função objetivo e restrições. Análises modais das topologias ótimas são utilizadas para a definição de um controlador LQR e as respostas das estruturas controladas submetidas à uma carga impulsiva são analisadas.
This work presents a topology optimization formulation for the actuator placement based on the control theory. The structure is composed by two materials: a passive elastic material and an active piezoelectric material, both linear. The aim is to obtain a control system which all states are controllable. The topology optimization process searches the piezoelectric material distribution which maximizes the smallest eigenvalue of the controllability Gramian ensuring its non-singularity and, therefore, the system is completely controllable. Sequential linear programming (SLP) is used to solve the optimization problem. The sensitivities for the finite element model were derived for the objective function and constraints. Modal analysis from the optimal topologies were employed in an LQR controller and the responses for the controlled structures submitted to an impulsive load are analyzed.
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Roy, Prateep Kumar. "Analysis & design of control for distributed embedded systems under communication constraints." Phd thesis, Université Paris-Est, 2009. http://tel.archives-ouvertes.fr/tel-00534012.

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Les Systèmes de Contrôle Embarqués Distribués (SCED) utilisent les réseaux de communication dans les boucles de rétroaction. Étant donné que les systèmes SCED ont une puissance de batterie, une bande passante de communication et une puissance de calcul limitée, les débits des données ou des informations transmises sont bornées et ils peuvent affecter leur stabilité. Ceci nous amène à élargir le spectre de notre étude et y intégrer une étude sur la relation entre la théorie du contrôle d'un coté et celle de l'information de l'autre. La contrainte de débit de données induit la quantification des signaux tandis que les aspects de calcul temps réel et de communication induit des événements asynchrones qui ne sont plus réguliers ou périodiques. Ces deux phénomènes donnent au SCED une double nature, continue et discrète, et en font des cas d'étude spécifiques. Dans cette thèse, nous analysons la stabilité et la performance de SCED du point de vue de la théorie de l'information et du contrôle. Pour les systèmes linéaires, nous montrons l'importance du compromis entre la quantité d'information communiquée et les objectifs de contrôle, telles que la stabilité, la contrôlabilité/observabilité et les performances. Une approche de conception conjointe de contrôle et de communication (en termes de débit d'information au sens de Shannon) des SCED est étudiée. Les principaux résultats de ces travaux sont les suivants : nous avons prouvé que la réduction d'entropie (ce qui correspond à la réduction d'incertitude) dépend du Grammien de contrôlabilité. Cette réduction est également liée à l'information mutuelle de Shannon. Nous avons démontré que le Grammien de contrôlabilité constitue une métrique de l'entropie théorique de l'information en ce qui concerne les bruits induits par la quantification. La réduction de l'influence de ces bruits est équivalente à la réduction de la norme du Grammien de contrôlabilité. Nous avons établi une nouvelle relation entre la matrice d'information de Fisher (FIM) et le Grammien de Contrôlabilité (CG) basé sur la théorie de l'estimation et la théorie de l'information. Nous proposons un algorithme qui distribue de manière optimale les capacités de communication du réseau entre un nombre "n" d'actionneurs et/ou systèmes concurrents se basant sur la réduction de la norme du Grammien de Contrôlabilité
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Book chapters on the topic "Controllability gramian"

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Nabi-Abdolyousefi, Marzieh. "Controllability Gramian, Symmetry Structures, and Application of Circulant Networks." In Controllability, Identification, and Randomness in Distributed Systems, 69–77. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02429-5_6.

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Gusev, Mikhail. "Estimates of the Minimal Eigenvalue of the Controllability Gramian for a System Containing a Small Parameter." In Mathematical Optimization Theory and Operations Research, 461–73. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-22629-9_32.

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Gusev, Mikhail. "Asymptotic Behaviour of Controllability Gramians and Convexity of Small-Time Reachable Sets." In Large-Scale Scientific Computing, 48–55. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-41032-2_5.

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Bourquin, Frédéric, José Urquiza, and Rabah Namar. "Discretization of the Controllability Grammian in View of Exact Boundary Control: the Case of Thin Plates." In Optimal Control of Partial Differential Equations, 53–62. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8691-8_5.

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Conference papers on the topic "Controllability gramian"

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Preciado, Victor M., and M. Amin Rahimian. "Controllability Gramian spectra of random networks." In 2016 American Control Conference (ACC). IEEE, 2016. http://dx.doi.org/10.1109/acc.2016.7525517.

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Roy, Sandip, and Mengran Xue. "Controllability-Gramian Submatrices for a Network Consensus Model." In 2019 IEEE 58th Conference on Decision and Control (CDC). IEEE, 2019. http://dx.doi.org/10.1109/cdc40024.2019.9030069.

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Roy, Prateep, Arben Cela, and Yskandar Hamam. "On the relation of FIM and Controllability Gramian." In 2009 IEEE International Symposium on Industrial Embedded Systems (SIES). IEEE, 2009. http://dx.doi.org/10.1109/sies.2009.5196189.

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Hauksdottir, Anna Soffia, and Sven P. Sigurdsson. "The continuous closed form controllability Gramian and its inverse." In 2009 American Control Conference. IEEE, 2009. http://dx.doi.org/10.1109/acc.2009.5160123.

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He, Bin-Bin, YangQuan Chen, and Chun-Hai Kou. "On the Controllability of Distributed-Order Fractional Systems With Distributed Delays." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67685.

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This paper investigates the controllability of distributed-order fractional systems with distributed delays. By using the controllability Gramian matrix and reduction to absurdity, a necessary and sufficient condition for the controllability of linear system is established, and a sufficient condition for the nonlinear system is obtained. Examples are given to illustrate the effectiveness of the theorems.
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Gupta, Rikin, Wei Zhao, and Rakesh K. Kapania. "Investigation of Controllability Gramian as Control Objective in MDAO Framework." In AIAA Aviation 2019 Forum. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2019. http://dx.doi.org/10.2514/6.2019-3550.

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Chanekar, Prasad Vilas, and Jorge Cortes. "Edge Centrality Matrix: Impact of Network Modification on Gramian Controllability Metrics." In 2020 American Control Conference (ACC). IEEE, 2020. http://dx.doi.org/10.23919/acc45564.2020.9147504.

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Halevi, Yoram. "An Efficient Approximated Algorithm for Balancing and Order Reduction of Lightly Damped Systems." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0685.

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Abstract A method of approximating the controllability gramian, observability gramian and the balancing transformation for lightly damped mechanical systems is presented, the approximation uses the special structure of the system and the fact that the damping is small to reduce the amount of computation considerably. Furthermore, one can avoid the calculation of the entire balancing transformation matrix and calculate only the parts that are required for order reduction. In cases where the reduced order is much smaller than the original that leads to another substantial reduction of computation effort.
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Nguyen, Dang Toan, and Didier Georges. "Controllability Gramian for Optimal Placement of Power System Stabilizers in Power Systems." In APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems. IEEE, 2006. http://dx.doi.org/10.1109/apccas.2006.342439.

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Gonçalves, Juliano F., Daniel M. De Leon, and Jun S. O. Fonseca. "A comparison study on actuator topology optimization designs using the controllability Gramian." In XXXVI Iberian Latin American Congress on Computational Methods in Engineering. Rio de Janeiro, Brazil: ABMEC Brazilian Association of Computational Methods in Engineering, 2015. http://dx.doi.org/10.20906/cps/cilamce2015-0240.

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