Dans cette thèse nous avons étudié différents aspects pour le contrôle de systèmes hyperboliques.Tout d'abord, nous nous sommes intéressés à des systèmes hyperboliques à commutations. Cela signifie qu'il existe une interaction entre une dynamique continue et une dynamique discrète. Autrement dit, il existe différents modes dans lesquels peut évoluer la dynamique continue: ces modes sont dictés par la dynamique discrète. Ce changement de mode peut être contrôlé (dans le cas d'une boucle fermée), ou non-contrôlé (dans le cas d'une boucle ouverte). Nous nous sommes intéressés au premier cas. Par une analyse Lyapunov nous avons construit trois règles de commutations capables de stabiliser le système. Nous avons montré comment modifier deux d'entre elles pour obtenir des propriétés de robustesse et de stabilité entrée-état. Ces règles de commutations ont été testées numériquement.Ensuite, nous avons considéré la génération de trajectoire pour des systèmes hyperboliques linéaires 2x2 par backstepping. L'étape suivante a été de considérer une action Proportionnelle-Intégrale pour stabiliser la solution du système autour de la trajectoire de référence. Pour cela nous avons construit une fonction Lyapunov non-diagonale. Nous avons montré que l'action intégrale est capable de rejeter des erreurs distribuées et frontières.Enfin, nous avons considéré des aspects numériques pour l'analyse Lyapunov. Les conditions pour la stabilité et la conception de contrôleurs obtenues par des fonctions de Lyapunov quadratiques font intervenir une infinité d'inégalités matricielles. Nous avons montré que cette complexité peut être réduite en considérant une sur-approximation polytopique de ces contraintes.Les résultats obtenus ont été illustrés par des exemples académiques et des systèmes dynamiques physiques (comme les équations de Saint-Venant et les équations de Aw-Rascle-Zhang). / In this thesis we have considered different aspects for the control of hyperbolic systems.First, we have studied switched hyperbolic systems. They contain an interaction between a continuous and a discrete dynamics. Thus, the continuous dynamics may evolve in different modes: these modes are imposed by the discrete dynamics. The change in the mode may be controlled (in case of a closed-loop system), or may be uncontrolled (in case of an open-loop system). We have focused our interest on the former case. We procedeed with a Lyapunov analysis, and construct three switching rules. We have shown how to modify them to get robustness and ISS properties. We have shown their effectiveness with numerical tests.Then, we have considered the trajectory generation problem for 2x2 linear hyperbolic systems. We have solved it with backstepping. Then, we have considered the tracking problem with a Proportionnal-Integral controller. We have shown that it stabilizes the error system around the reference trajectory with a new non-diagonal Lyapunov function. The integral action has been shown to be able to reject in-domain, as well as boundary disturbances.Finally, we have considered numerical aspects for the Lyapunov analysis. The conditions for the stability and design of controllers by quadratic Lyapunov functions involve an infinity of matrix inequalities. We have shown how to reduce this complexity by polytopic embeddings of the constraints.Many obtained results have been illustrated by academic examples and physically relevant dynamical systems (as Shallow-Water equations and Aw-Rascle-Zhang equations).

Motivée par les travaux précédents sur la stabilisation de systèmes à excitation persistante, cette thèse s'intéresse à la stabilité et à la stabilisation de systèmes linéaires à commutation en dimensions finie et infinie. Après une introduction générale présentant les principales motivations et les résultats importants de la littérature, on aborde quatre sujets.On commence par l'étude d'un système linéaire en dimension finie à commutation aléatoire. Le temps passé en chaque sous-système $i$ est choisi selon une loi de probabilité ne dépendant que de $i$, les commutations entre sous-systèmes étant déterminées par une chaine de Markov discrète. On caractérise les exposants de Lyapunov en appliquant le Théorème Ergodique Multiplicatif d'Oseledets à un système associé en temps discret, et on donne une expression pour l'exposant de Lyapunov maximal. Ces résultats sont appliqués à un système de contrôle à commutation. Sous une hypothèse de contrôlabilité, on montre que ce système peut être stabilisé presque surement avec taux de convergence arbitraire, ce qui est en contraste avec les systèmes déterministes à excitation persistante.On considère ensuite un système de $N$ équations de transport avec amortissement interne à excitation persistante, couplées linéairement par le bord à travers une matrice $M$, ce qui peut être vu comme un système d'EDPs sur un réseau étoilé. On montre que, si l'activité de l'amortissement intermittent est déterminée par des signaux à excitation persistante, alors, sous des bonnes hypothèses sur $M$ et sur la rationalité des rapports entre les longueurs des arêtes du réseau, ce système est exponentiellement stable, uniformément par rapport aux signaux à excitation persistante. Ce résultat est montré grâce à une formule explicite pour les solutions du système, qui permet de bien suivre les effets de l'amortissement intermittent.Le sujet suivant que l'on considère est le comportement asymptotique d'équations aux différences non-autonomes. On obtient une formule explicite pour les solutions en termes des conditions initiales et de certains coefficients matriciels dépendants du temps, qui généralise la formule obtenue pour le système de $N$ équations de transport. Le comportement asymptotique des solutions est caractérisé à travers les coefficients matriciels. Dans le cas d'équations aux différences à commutation arbitraire, on obtient un résultat de stabilité qui généralise le critère de Hale--Silkowski pour les systèmes autonomes. Grâce à des transformations classiques d'EDPs hyperboliques en équations aux différences, on applique ces résultats au transport et à la propagation d'ondes sur des réseaux.Finalement, la formule explicite précédente est généralisée à une équation aux différences contrôlée, dont la contrôlabilité est alors analysée. La contrôlabilité relative est caractérisée à travers un critère algébrique sur les coefficients matriciels de la formule explicite, ce qui généralise le critère de Kalman. On compare également la contrôlabilité relative pour des retards différents en termes de leur structure de dépendance rationnelle, et on donne une borne sur le temps minimal de contrôlabilité. Pour des systèmes avec retards commensurables, on montre que la contrôlabilité exacte est équivalente à l'approchée et on donne un critère qui les caractérise. On analyse également la contrôlabilité exacte et approchée de systèmes en dimension $2$ avec deux retards sans l'hypothèse de commensurabilité. / Motivated by previous work on the stabilization of persistently excited systems, this thesis addresses stability and stabilization issues for linear switched systems in finite and infinite dimensions. After a general introduction presenting the main motivations and important results from the literature, we analyze four problems.The first system we study is a linear finite-dimensional random switched system. The time spend on each subsystem $i$ is chosen according to a probability law depending only on $i$, and the switches between subsystems are determined by a discrete Markov chain. We characterize the Lyapunov exponents by applying Oseledets' Multiplicative Ergodic Theorem to an associated discrete-time system, and provide an expression for the maximal Lyapunov exponent. These results are applied to a switched control system, showing that, under a controllability hypothesis, almost sure stabilization can be achieved with arbitrarily large decay rates, a situation in contrast to deterministic persistently excited systems.We next consider a system of $N$ transport equations with intermittent internal damping, linearly coupled by their boundary conditions through a matrix $M$, which can be seen as a system of PDEs on a star-shaped network. We prove that, if the activity of the intermittent damping terms is determined by persistently exciting signals, then, under suitable hypotheses on $M$ and on the rationality of the ratios between the lengths of the network edges, such system is exponentially stable, uniformly with respect to the persistently exciting signals. The proof of this result is based on an explicit representation formula for the solutions of the system, which allows one to efficiently track down the effects of the intermittent damping.The following topic we address is the asymptotic behavior of non-autonomous difference equations. We obtain an explicit representation formula for their solutions in terms of their initial conditions and some time-dependent matrix coefficients, which generalizes the one for the system of $N$ transport equations. The asymptotic behavior of solutions is characterized in terms of the matrix coefficients. In the case of difference equations with arbitrary switching, we obtain a stability result which generalizes Hale--Silkowski criterion for autonomous systems. Using classical transformations of hyperbolic PDEs into difference equations, we apply our results to transport and wave propagation on networks.Finally, we generalize the previous representation formula to a controlled difference equation, whose controllability is then analyzed. Relative controllability is characterized in terms of an algebraic property on the matrix coefficients from the explicit formula, generalizing Kalman criterion. We also compare the relative controllability for different delays in terms of their rational dependence structure, and provide a bound on the minimal controllability time. Exact and approximate controllability for systems with commensurable delays are characterized and proved to be equivalent. We also describe exact and approximate controllability for two-dimensional systems with two delays not necessarily commensurable.

No description available.

A platoon of autonomous underwater vehicles provides a compelling platform for studying many challenging issues in multi-agent cooperative control. These challenges include developing cooperative algorithms suitable to practical multi-vehicle applications. They also include addressing intervehicle communication issues, such as sharing information via limited bandwidth channels and selecting network architecture to facilitate control design. This work addresses problems in each of these areas. Environmental tracking and formation control serves as the main application upon which this work focuses. In the tracking and formation control application, a team of vehicles obtains a spatial average of an environmental feature by collecting and sharing local measurements. To achieve this objective, vehicles track a desired environmental field contour with their average position while maintaining a desired spatial formation about the average. A decentralized consensus-based algorithm is developed for controlling the platoon. In a novel two-level consensus approach, each vehicle estimates a virtual leader trajectory using local and shared measurements at one level, then positions itself about the virtual leader at a second level. Due to very low bandwidth underwater communication, vehicles share information intermittently, and the platoon network is effectively disconnected at every instant of time. This issue is addressed by modeling the platoon as a periodic switched system whose frozen-time subsystems possess disconnected networks, but whose time-averaged system is connected. The stability and input-output properties of the switched system are related to those of the corresponding average system. Under sufficiently fast switching, asymptotic stability of the average system implies asymptotic stability of the switched system and the existence of an L2 gain. Estimates of the slowest stabilizing switching rate and the L2 gain are derived. Controller and estimator design are complicated by the lack of a separation principle for decentralized systems and by the effects of intervehicle coupling. The potential for choosing the communication topology in a manner that leads to design simplifications is investigated. In particular, a transformation is presented that converts the platoon state coefficient matrix to block diagonal form when the communication network has a circulant structure. / Ph. D.

Les travaux de cette thèse portent sur l’analyse de stabilité et la synthèse de commandes robustes pour les systèmes linéaires à commutation en temps discret avec des incertitudes polytopiques et des incertitudes sur la loi de commutation. On considère des lois de commutations arbitraires et on montre que l’utilisation des fonctions de Lyapunov commutées dépendant de paramètres permet de déterminer des critères de stabilité et de stabilisation robuste moins conservatifs. Ensuite, des conditions de stabilité robuste pour les systèmes en temps discret avec une loi de commutation incertaine sont présentées en termes de temps minimum de séjour. Les résultats obtenus s’avèrent utiles dans le contexte de la commande numérique des systèmes continus en présence d’imprécisions sur les instants d’échantillonnage et d’application des commandes. Nous montrons comment une modélisation à base d’évènements permet de ramener le problème original à un problème spécifique aux systèmes à commutation avec des incertitudes polytopiques. Les résultats sont étendus au cas des systèmes à commutation continus commandés par des correcteurs numériques / This PhD thesis is dedicated to the study of robust stability analysis and control synthesis for discrete time uncertain switching systems under arbitrary switching. Polytopic uncertainties are considered. We show that Lyapunov functions that depend on the uncertain parameter and that take into account the structure of the system may be used in order to reduce the conservatism related to uncertainty problems. Next, we consider the case of discrete time switched systems that are stabilized by a switched state feedback for which the switching signal may be temporary uncertain. Dwell time conditions for stability analysis of such systems are given. These results are usefull in the context of continuous time are stabilized via a computer when uncertainties occur on the sampling and actuation events. We present a new event based discrete-time model and we show that the stabilizability of this system can be achieved by finding a control for a switched polytopic system. The methodology is extended to the case of switched system

Orientador: José Cláudio Geromel / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-16T14:10:01Z (GMT). No. of bitstreams: 1 Deaecto_GraceSilva_D.pdf: 2021318 bytes, checksum: 451e6647afe6d7beac67cf3717dff7da (MD5) Previous issue date: 2010 / Resumo: Esta tese trata do projeto de controladores dinâmicos H2 ou H? via realimentação de saída para sistemas lineares com comutação contínuos e discretos no tempo. Inicialmente, apresentamos a síntese via realimentação de estado de forma a colocar em evidência as principais dificuldades para a obtenção da solução do problema de projeto mais realista, correspondente ao controle via realimentação dinâmica de saída. As condições obtidas são necessárias e suficientes para a existência de solução com uma estrutura particular para as chamadas desigualdades de Lyapunov ou Riccati-Metzler. Tratamos também da síntese via realimentação de estado de sistemas sujeitos a incertezas limitadas em norma e politópicas. No que diz respeito às incertezas limitadas em norma, as condições são válidas inclusive se as mesmas apresentarem estrutura do tipo linear fracionária (LFT). No caso de incertezas politópicas, as condições podem ser empregadas como uma alternativa para o projeto de controle de sistemas com parâmetros lineares variantes no tempo (LPV). Aplicamos os resultados teóricos para a solução de três problemas de cunho essencialmente práticos, a saber, a regulação da tensão de saída de conversores de potência CCCC, a estimação da aceleração vertical de uma suspensão automotiva e o controle do ângulo de rolamento de uma aeronave / Abstract: This thesis is concerned to the output feedback H2 or H? control design for continuous-time and discrete-time switched linear systems. Initially, we present the state feedback synthesis in order to put in evidence the main difficulties we have to face towards the solution of the more realistic output feedback control design problem. The conditions are necessary and sufficient regarding the existence of a structured solution of the Lypunov or Riccati-Metzler inequalities. We also treat the state feedback synthesis for switched linear systems subject to norm bounded or polytopic uncertainties. In the former case, the conditions hold even if the uncertainty presents the linear fractional structure (LFT), and in the latter one, the conditions can be used as an alternative to the linear parameter varying control (LPV). The theoretical results are applied to three practical problems, namely, the output voltage regulation of DC-DC converters, the vertical stroke estimation in automotive suspensions and aircraft roll angle control / Doutorado / Automação / Doutor em Engenharia Elétrica

Orientador: Jose Claudio Geromel / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-09T08:47:02Z (GMT). No. of bitstreams: 1 Deaecto_GraceSilva_M.pdf: 5350126 bytes, checksum: 88f05b9392a9876bfe07fae6a8f95202 (MD5) Previous issue date: 2007 / Resumo: Neste trabalho, são propostas condições suficientes para a estabilidade assintótica de sistemas lineares, contínuos no tempo, com comutação que asseguram um custo garantido de desempenho. Estas condições dependem da solução de um conjunto de desigualdades de Lyapunov-Metzler, definidas em [Geromel & Colaneri, 2006], que possuem natureza não-convexa, sendo portanto, de difícil solução. Para contornar este problema, apresentamos condições de estabilidade mais conservadoras baseadas em uma subclasse de matrizes de Metzler com elementos iguais na diagonal principal, que podem ser resolvidas através de desigualdades matriciais lineares e busca unidimensional. Os resultados apresentados em [Geromel & Colaneri, 2006], que fornecem condições para a estabilidade de sistemas dinâmicos lineares com comutação, são generalizados para lidar com sistemas mais gerais, a saber, sistemas dinâmicos sujeitos a perturbações impulsivas. A proposta elaborada assegura a estabilidade assintótica inclusive na presença de possíveis modos deslizantes / Abstract: In this work, sufficient conditions are proposed for the study of asymptotic stability of continuous time linear systems with commutation, which assure a guaranteed cost of performance. These conditions depend on the solution of a set of Lyapunov-Metzler inequalities, defined in [Geromel & Colaneri, 2006], which are difficult to solve due to their non-convex nature. However, to circumvent this difficulty, we present more conservative stability conditions based on a subclass of Metzler matrices characterized by having equal elements on the main diagonal. Although these conditions are more conservative, they can be solved by Linear Matrix Inequalities (LMls) and unidimensional search. The analysis done in [Geromel & Colaneri, 2006], which provides the stability conditions for linear dynamic systems with commutation is expanded to cover a more general class of systems with commutation and subject to impulsive disturbances. The conditions presented in this work assure the stability even in the presence of possible sliding modes / Mestrado / Automação / Mestre em Engenharia Elétrica

Orientador: José Cláudio Geromel / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-20T09:26:11Z (GMT). No. of bitstreams: 1 Souza_Matheus_M.pdf: 1860153 bytes, checksum: d0e172f3d6ad34ab1ec2e31a48ab171d (MD5) Previous issue date: 2012 / Resumo: Nesta dissertação, são propostas técnicas de projeto de controladores...Observação: O resumo, na íntegra, poderá ser visualizado no texto completo da tese digital / Abstract: In this dissertation, state feedback...Note: The complete abstract is available with the full electronic document / Mestrado / Automação / Mestre em Engenharia Elétrica

Orientador: Grace Silva Deaecto / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-27T00:51:44Z (GMT). No. of bitstreams: 1 Santos_GuilhermeCavalari_M.pdf: 16424850 bytes, checksum: 7f2f16f9c4c4f920f928c8d19273978a (MD5) Previous issue date: 2015 / Resumo: Esta dissertação trata do projeto de controle H2 e Hoo via realimentação de estado para sistemas afins com comutação a tempo contínuo. Nosso objetivo principal é projetar um conjunto de ganhos de realimentação de estado e uma função de comutação assegurando estabilidade assintótica global do ponto de equilíbrio desejado. Este ponto deve pertencer a um conjunto de pontos de equilíbrio atingíveis a ser determinado. Além disso, o projeto deve levar em conta índices de desempenho H2 e Hoo que são adequadamente definidos. Para o projeto de controle Hoo, duas funções de comutação são propostas e discutidas. A primeira delas depende somente do estado, enquanto a segunda representa uma nova proposta que é mais geral e depende também da entrada externa. As condições obtidas são menos conservadoras do que as técnicas recentes disponíveis na literatura, por exemplo, os métodos baseados na função de Lyapunov do tipo máximo e os utilizados normalmente para assegurar estabilidade prática. Exemplos numéricos ilustram os resultados teóricos obtidos e são usados para comparações / Abstract: This Master's thesis deals with state feedback H2 and Hoo control design of continuous-time switched affine systems. Our main goal is to design a set of state feedback gains and a switching function assuring global asymptotical stability of a desired equilibrium point. This point must belong to a set of attainable equilibrium points to be determined. Moreover, the design must consider H2 and Hoo performance indexes to be defined. For the Hoo control design, two different switching functions are proposed and discussed. The first one depends only on the state and the other depends on the state and on the external input. The conditions are less conservative than the techniques available in the literature to date, as for instance, those based on a max-type Lyapunov function and those commonly used to assure practical stability. Numerical examples illustrate the theoretical results and are used for comparisons / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

Orientador: Grace Silva Deaecto / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-27T16:26:54Z (GMT). No. of bitstreams: 1 Suto_AlanPereira_M.pdf: 1433599 bytes, checksum: 847a72c2f990c5ca185477889617c8ff (MD5) Previous issue date: 2015 / Resumo: Esta dissertação trata do controle H2 de sistemas com comutação do tipo Lur¿e baseado no critério generalizado de Popov. Mais especificamente, uma nova regra de comutação dependente do estado e da entrada externa é proposta de tal forma a assegurar estabilidade assintótica global e um custo garantido H2 de desempenho. Esta nova estratégia de comutação é o ponto chave para a generalização do célebre critério de Popov. Como no caso de sistemas invariantes no tempo, propomos um teste de estabilidade baseado no domínio da frequência expresso em termos de uma certa combinação convexa das matrizes de espaço de estado dos subsistemas. Ademais, este teste leva em conta a inclusão de um índice de desempenho H2 cujo estudo, no presente contexto, é inédito na literatura. Os resultados teóricos obtidos são aplicados no controle de uma suspensão semi-ativa automotiva evidenciando a validade e a eficiência da função de comutação proposta / Abstract: This Master¿s dissertation deals with H2 control design of Lur¿e-type switched systems based on the generalized Popov criterion. More specifically, a novel state-input dependent switching rule is proposed in order to assure global asymptotic stability and an H2 guaranteed cost. This new switching strategy is the key issue to generalize the celebrated Popov criterion. Likewise the case of time invariant systems, we propose a frequency domain stability test that is expressed in terms of a certain convex combination of the subsystems state space matrices. Moreover, this test takes into account an H2 performance index whose study, in the present context, is new in the literature. The theoretical results are used to the control design of a car semiactive suspension and to put in evidence the validity and the efficiency of the proposed switching function / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica