Prieur, Christophe
Overview
Works:  48 works in 76 publications in 2 languages and 632 library holdings 

Roles:  Editor, Author, Thesis advisor, Other, Opponent, htt, Contributor, Composer 
Classifications:  QA402.35, 629.8 
Publication Timeline
.
Most widely held works by
Christophe Prieur
Safety factor profile control in a tokamak by
Federico Bribiesca Argomedo(
)
14 editions published between 2013 and 2014 in English and held by 376 WorldCat member libraries worldwide
Control of the Safety Factor Profile in a Tokamak uses Lyapunov techniques to address a challenging problem for which even the simplest physically relevant models are represented by nonlinear, timedependent, partial differential equations (PDEs). This is because of the spatiotemporal dynamics of transport phenomena (magnetic flux, heat, densities, etc.) in the anisotropic plasma medium. Robustness considerations are ubiquitous in the analysis and control design since direct measurements on the magnetic flux are impossible (its estimation relies on virtual sensors) and large uncertainties remain in the coupling between the plasma particles and the radiofrequency waves (distributed inputs). The Brief begins with a presentation of the reference dynamical model and continues by developing a Lyapunov function for the discretized system (in a polytopic linearparametervarying formulation). The limitations of this finitedimensional approach motivate new developments in the infinitedimensional framework. The text then tackles the construction of an inputtostatestabilityLyapunov function for the infinitedimensional system that handles the medium anisotropy and provides a common basis for analytical robustness results. This function is used as a controlLyapunov function and allows the amplitude and nonlinear shape constraints in the control action to be dealt with. Finally, the Brief addresses important application and implementationspecific concerns. In particular, the coupling of the PDE and the finitedimensional subsystem representing the evolution of the boundary condition (magnetic coils) and the introduction of profilereconstruction delays in the control loop (induced by solving a 2D inverse problem for computing the magnetic flux) is analyzed. Simulation results are presented for various operation scenarios on Tore Supra (simulated with METIS) and on TCV (simulated with RAPTOR). Control of the Safety Factor Profile in a Tokamak will be of interest to both academic and industriallybased researchers interested in nuclear energy and plasmacontainment control systems, and graduate students in nuclear and control engineering.
14 editions published between 2013 and 2014 in English and held by 376 WorldCat member libraries worldwide
Control of the Safety Factor Profile in a Tokamak uses Lyapunov techniques to address a challenging problem for which even the simplest physically relevant models are represented by nonlinear, timedependent, partial differential equations (PDEs). This is because of the spatiotemporal dynamics of transport phenomena (magnetic flux, heat, densities, etc.) in the anisotropic plasma medium. Robustness considerations are ubiquitous in the analysis and control design since direct measurements on the magnetic flux are impossible (its estimation relies on virtual sensors) and large uncertainties remain in the coupling between the plasma particles and the radiofrequency waves (distributed inputs). The Brief begins with a presentation of the reference dynamical model and continues by developing a Lyapunov function for the discretized system (in a polytopic linearparametervarying formulation). The limitations of this finitedimensional approach motivate new developments in the infinitedimensional framework. The text then tackles the construction of an inputtostatestabilityLyapunov function for the infinitedimensional system that handles the medium anisotropy and provides a common basis for analytical robustness results. This function is used as a controlLyapunov function and allows the amplitude and nonlinear shape constraints in the control action to be dealt with. Finally, the Brief addresses important application and implementationspecific concerns. In particular, the coupling of the PDE and the finitedimensional subsystem representing the evolution of the boundary condition (magnetic coils) and the introduction of profilereconstruction delays in the control loop (induced by solving a 2D inverse problem for computing the magnetic flux) is analyzed. Simulation results are presented for various operation scenarios on Tore Supra (simulated with METIS) and on TCV (simulated with RAPTOR). Control of the Safety Factor Profile in a Tokamak will be of interest to both academic and industriallybased researchers interested in nuclear energy and plasmacontainment control systems, and graduate students in nuclear and control engineering.
Trends in nonlinear and adaptive control : a tribute to Laurent Praly for his 65th birthday by
Z.P Jiang(
)
6 editions published between 2021 and 2022 in English and held by 121 WorldCat member libraries worldwide
This book, published in honor of Professor Laurent Praly on the occasion of his 65th birthday, explores the responses of some leading international authorities to new challenges in nonlinear and adaptive control. The mitigation of the effects of uncertainty and nonlinearity  ubiquitous features of realworld engineering and natural systems  on closedloop stability and robustness being of crucial importance, the contributions report the latest research into overcoming these difficulties in: autonomous systems; reset control systems; multipleinputmultipleoutput nonlinear systems; input delays; partial differential equations; population games; and datadriven control. Trends in Nonlinear and Adaptive Control presents research inspired by and related to Professor Praly's lifetime of contributions to control theory and is a valuable addition to the literature of advanced control
6 editions published between 2021 and 2022 in English and held by 121 WorldCat member libraries worldwide
This book, published in honor of Professor Laurent Praly on the occasion of his 65th birthday, explores the responses of some leading international authorities to new challenges in nonlinear and adaptive control. The mitigation of the effects of uncertainty and nonlinearity  ubiquitous features of realworld engineering and natural systems  on closedloop stability and robustness being of crucial importance, the contributions report the latest research into overcoming these difficulties in: autonomous systems; reset control systems; multipleinputmultipleoutput nonlinear systems; input delays; partial differential equations; population games; and datadriven control. Trends in Nonlinear and Adaptive Control presents research inspired by and related to Professor Praly's lifetime of contributions to control theory and is a valuable addition to the literature of advanced control
ANALYSIS AND SYNTHESIS OF RESET CONTROL SYSTEMS by
Christophe Prieur(
Book
)
3 editions published between 2016 and 2018 in English and held by 34 WorldCat member libraries worldwide
This monograph gives an indepth assessment of the stateoftheart and provides the reader with a starting point for further research into the increasingly important topic of Reset Control Systems
3 editions published between 2016 and 2018 in English and held by 34 WorldCat member libraries worldwide
This monograph gives an indepth assessment of the stateoftheart and provides the reader with a starting point for further research into the increasingly important topic of Reset Control Systems
Trends in Nonlinear and Adaptive Control : A Tribute to Laurent Praly for his 65th Birthday(
)
2 editions published in 2022 in English and held by 31 WorldCat member libraries worldwide
2 editions published in 2022 in English and held by 31 WorldCat member libraries worldwide
Contrôle et stabilité EntréeEtat en dimension infinie du profil du facteur de sécurité dans un plasma Tokamak by
Federico Bribiesca Argomedo(
)
2 editions published in 2012 in French and English and held by 3 WorldCat member libraries worldwide
In this thesis, we are interested in the control of the safety factor profile or qprofile in a tokamak plasma. This physical quantity has been found to be related to several phenomena in the plasma, in particular magnetohydrodynamic (MHD) instabilities. Having an adequate safety factor profile is particularly important to achieve advanced tokamak operation, providing high confinement and MHD stability. To achieve this, we focus in controlling the gradient of the poloidal magnetic flux profile. The evolution of this variable is given by a diffusion equation with distributed timevarying coefficients. Based on Lyapunov techniques and the InputtoState stability properties of the system we propose a robust control law that takes into account nonlinear constraints on the control action imposed by the physical actuators
2 editions published in 2012 in French and English and held by 3 WorldCat member libraries worldwide
In this thesis, we are interested in the control of the safety factor profile or qprofile in a tokamak plasma. This physical quantity has been found to be related to several phenomena in the plasma, in particular magnetohydrodynamic (MHD) instabilities. Having an adequate safety factor profile is particularly important to achieve advanced tokamak operation, providing high confinement and MHD stability. To achieve this, we focus in controlling the gradient of the poloidal magnetic flux profile. The evolution of this variable is given by a diffusion equation with distributed timevarying coefficients. Based on Lyapunov techniques and the InputtoState stability properties of the system we propose a robust control law that takes into account nonlinear constraints on the control action imposed by the physical actuators
Mined individuals in large networks by
Christophe Prieur(
Book
)
1 edition published in 2015 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2015 in English and held by 3 WorldCat member libraries worldwide
Diverses méthodes pour des problèmes de stabilisation by
Christophe Prieur(
Book
)
2 editions published in 2001 in French and held by 3 WorldCat member libraries worldwide
In this thesis, we study some problems of stabilization in control theory for three different class of systems. First, for the nonlinear finitedimensional systems in presence of noise, we introduce a class of hybrid controllers with a mixed continuous/discrete state. Given a system with a globally asymptotically controllable equilibrium, we prove that there exists such a control such that the equilibrium is globally asympotically stable with a robustness property with respect to small perturbations. For the chained systems we explicit such a feeback with only one discrete variable.We give also a hybrid control and a timevarying control which unit robustly any pair of continuous feedbacks and renders the origin a globally asymptotically stable equilibrium. Secondly, we study the stabilization problem of the tank containing a fluid subject. It is subject to a horizontal move. It is a infinitedimensional control problem because we describe the system by using the shallow water equations which are hyperbolic partial differential equations
2 editions published in 2001 in French and held by 3 WorldCat member libraries worldwide
In this thesis, we study some problems of stabilization in control theory for three different class of systems. First, for the nonlinear finitedimensional systems in presence of noise, we introduce a class of hybrid controllers with a mixed continuous/discrete state. Given a system with a globally asymptotically controllable equilibrium, we prove that there exists such a control such that the equilibrium is globally asympotically stable with a robustness property with respect to small perturbations. For the chained systems we explicit such a feeback with only one discrete variable.We give also a hybrid control and a timevarying control which unit robustly any pair of continuous feedbacks and renders the origin a globally asymptotically stable equilibrium. Secondly, we study the stabilization problem of the tank containing a fluid subject. It is subject to a horizontal move. It is a infinitedimensional control problem because we describe the system by using the shallow water equations which are hyperbolic partial differential equations
Conebounded feedback laws for mdissipative operators on Hilbert spaces by
Swann Marx(
)
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
Problèmes de stabilisation au bord pour des systèmes d'équations aux dérivées partielles hyperboliques en dimension un
d'espace by
Mathias Dus(
Book
)
2 editions published in 2021 in English and held by 2 WorldCat member libraries worldwide
In this thesis, we study the problem of boundary stabilization of general hyperbolic systems of partial differential equations. More precisely, the analysis focuses on systems where the transport term is scalar and for which the information propagates in a fixed direction. In addition, the chosen control is most of the time a state feedback law for which a saturation is possibly applied. The work is divided into two distinct parts, one focusing on Lyapunov techniques while the other one uses the linearity of the problem. In the first part of the thesis, two main works are presented. In the first one, only linear transport equations with positive velocities are considered. The main goal is to design a saturated linear feedback in order to stabilize exponentially the openloop system in L 8 . The method consists of using classical Lyapunov techniques to exhibit a basin of attraction for which a fine estimate is given. We also extend this work to nonlinear scalar conservation laws in a BV framework. In the other work, thanks to a slope limiter scheme, a system of scalar conservation laws is discretized. Inspired by "continuous" Lyapunov methods, a discrete Lyapunov functional is studied to prove the exponential BV stabilization of the discrete solution using a linear feedback. In the second part of the thesis, two works are exposed as well, this time in a full linear framework. On the one hand, we study systems of linear transport equations of arbitrary dimension, coupled on the domain and at the boundary. Designing a controller from a pole placement algorithm, the exponential stabilization is proved in L 2 . On the other hand, we develop a numerical Backstepping theory in order to stabilize in finite time a numerical scheme modeling a 2 × 2 linear system with in domain and boundary couplings
2 editions published in 2021 in English and held by 2 WorldCat member libraries worldwide
In this thesis, we study the problem of boundary stabilization of general hyperbolic systems of partial differential equations. More precisely, the analysis focuses on systems where the transport term is scalar and for which the information propagates in a fixed direction. In addition, the chosen control is most of the time a state feedback law for which a saturation is possibly applied. The work is divided into two distinct parts, one focusing on Lyapunov techniques while the other one uses the linearity of the problem. In the first part of the thesis, two main works are presented. In the first one, only linear transport equations with positive velocities are considered. The main goal is to design a saturated linear feedback in order to stabilize exponentially the openloop system in L 8 . The method consists of using classical Lyapunov techniques to exhibit a basin of attraction for which a fine estimate is given. We also extend this work to nonlinear scalar conservation laws in a BV framework. In the other work, thanks to a slope limiter scheme, a system of scalar conservation laws is discretized. Inspired by "continuous" Lyapunov methods, a discrete Lyapunov functional is studied to prove the exponential BV stabilization of the discrete solution using a linear feedback. In the second part of the thesis, two works are exposed as well, this time in a full linear framework. On the one hand, we study systems of linear transport equations of arbitrary dimension, coupled on the domain and at the boundary. Designing a controller from a pole placement algorithm, the exponential stabilization is proved in L 2 . On the other hand, we develop a numerical Backstepping theory in order to stabilize in finite time a numerical scheme modeling a 2 × 2 linear system with in domain and boundary couplings
Techniques d'analyse de stabilité et synthèse de contrôle pour des systèmes hyperboliques by
André Caldeira(
)
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
This work studies boundary control strategies for stability analysis and stabilization of firstorder hyperbolic system coupled with nonlinear dynamic boundary conditions. The modeling of a flow inside a pipe (fluid transport phenomenon) with boundary control strategy applied in a physical experimental setup is considered as a case study to evaluate the proposed strategies. Firstly, in the context of finite dimension systems, classical control tools are applied to deal with firstorder hyperbolic systems having boundary conditions given by the coupling of a heating column dynamical model and a ventilator static model. The tracking problem of this complex dynamics is addressed in a simple manner considering linear approximations, finite difference schemes and an integral action leading to an augmented discretetime linear system with dimension depending on the step size of discretization in space. Hence, for the infinite dimensional counterpart, two strategies are proposed to address the boundary control problem of firstorder hyperbolic systems coupled with nonlinear dynamic boundary conditions. The first one approximates the firstorder hyperbolic system dynamics by a pure delay. Then, convex stability and stabilization conditions of uncertain input delayed nonlinear quadratic systems are proposed based on the LyapunovKrasovskii (LK) stability theory which are formulated in terms of Linear Matrix Inequality (LMI) constraints with additional slack variables (introduced by the Finsler's lemma). Thus, strictly Lyapunov functions are used to derive an LMI based approach for the robust regional boundary stability and stabilization of firstorder hyperbolic systems with a boundary condition defined by means of a nonlinear quadratic dynamic system. The proposed stability and stabilization LMI conditions are evaluated considering several academic examples and also the flow inside a pipe as case study
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
This work studies boundary control strategies for stability analysis and stabilization of firstorder hyperbolic system coupled with nonlinear dynamic boundary conditions. The modeling of a flow inside a pipe (fluid transport phenomenon) with boundary control strategy applied in a physical experimental setup is considered as a case study to evaluate the proposed strategies. Firstly, in the context of finite dimension systems, classical control tools are applied to deal with firstorder hyperbolic systems having boundary conditions given by the coupling of a heating column dynamical model and a ventilator static model. The tracking problem of this complex dynamics is addressed in a simple manner considering linear approximations, finite difference schemes and an integral action leading to an augmented discretetime linear system with dimension depending on the step size of discretization in space. Hence, for the infinite dimensional counterpart, two strategies are proposed to address the boundary control problem of firstorder hyperbolic systems coupled with nonlinear dynamic boundary conditions. The first one approximates the firstorder hyperbolic system dynamics by a pure delay. Then, convex stability and stabilization conditions of uncertain input delayed nonlinear quadratic systems are proposed based on the LyapunovKrasovskii (LK) stability theory which are formulated in terms of Linear Matrix Inequality (LMI) constraints with additional slack variables (introduced by the Finsler's lemma). Thus, strictly Lyapunov functions are used to derive an LMI based approach for the robust regional boundary stability and stabilization of firstorder hyperbolic systems with a boundary condition defined by means of a nonlinear quadratic dynamic system. The proposed stability and stabilization LMI conditions are evaluated considering several academic examples and also the flow inside a pipe as case study
Commande optimale des systèmes de complémentarité linéaires by
Alexandre Vieira(
)
1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide
This thesis focuses on the optimal control of Linear Complementarity Systems (LCS). LCS are dynamical systems defined through Differential Algebraic Equations (DAE), where one of the variable is defined by a Linear Complementarity Problem.These systems can be found in the modeling of various phenomena, as Nash equilibria, hybrid dynamical systems or modeling of electrical circuits. Properties of the solution to these DAE essentially depend on properties that the matrix D in the complementarity must meet. These complementarity constraints induce two different challenges. First, the analysis of these dynamical systems often use state of the art tools, and their study still has some unansweredquestions. Second, the optimal control of these systems causes troubles due to on one hand the presence of the state in the constraints, on the other hand the violation of Constraint Qualifications, that are a recurring hypothesis for optimisation problems.The research presented in this manuscript focuses on the optimal control of these systems. We mainly focus on the quadratic optimal control problem (minimisation of a quadratic functional involving the state and the control), and the minimal time control. The results present two different aspects: first, we start with an analytical approach in order to find necessary conditions of optimality (if possible, these conditions are proved to be sufficient); secondly, a numerical approach is tackled, with the aim of getting precise results with a reduced computational time
1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide
This thesis focuses on the optimal control of Linear Complementarity Systems (LCS). LCS are dynamical systems defined through Differential Algebraic Equations (DAE), where one of the variable is defined by a Linear Complementarity Problem.These systems can be found in the modeling of various phenomena, as Nash equilibria, hybrid dynamical systems or modeling of electrical circuits. Properties of the solution to these DAE essentially depend on properties that the matrix D in the complementarity must meet. These complementarity constraints induce two different challenges. First, the analysis of these dynamical systems often use state of the art tools, and their study still has some unansweredquestions. Second, the optimal control of these systems causes troubles due to on one hand the presence of the state in the constraints, on the other hand the violation of Constraint Qualifications, that are a recurring hypothesis for optimisation problems.The research presented in this manuscript focuses on the optimal control of these systems. We mainly focus on the quadratic optimal control problem (minimisation of a quadratic functional involving the state and the control), and the minimal time control. The results present two different aspects: first, we start with an analytical approach in order to find necessary conditions of optimality (if possible, these conditions are proved to be sufficient); secondly, a numerical approach is tackled, with the aim of getting precise results with a reduced computational time
Active vibration control of a fluid/plate system by
Bogdan Robu(
Book
)
2 editions published in 2010 in English and held by 2 WorldCat member libraries worldwide
Cette thèse s'intéresse au problème du contrôle actif des vibrations structurelles d'une aile d'avion induites par le ballottement du carburant dans les réservoirs qu'elle contient. L'étude proposée ici est concentrée sur l'analyse d'un dispositif expérimental composé d'une longue plaque rectangulaire en aluminium équipée d'actionneurs et de capteurs piézoélectriques et d'un réservoir cylindrique. La difficulté principale réside dans le couplage complexe entre les modes de vibration de l'aile et les modes de ballottement du liquide. Un modèle de ce dispositif à l'aide d'équations aux dérivées partielles est tout d'abord construit. Ce modèle de dimension infinie couple une équation des plaques avec l'équation de Bernoulli pour le mouvement du fluide dans le réservoir. En analysant la contribution énergétique des modes, une approximation en dimension finie, de type espace d'état est alors construite. Après une méthode de recalage fréquentiel du modèle, un contrôle est réalisé en utilisant dans un premier temps une méthode par placement de pôle et dans un deuxième temps, la théorie de la commande robuste Hinfini. La dimension du modèle et les performances demandées imposent le calcul d'un contrôleur Hinfini d'ordre réduit, conçu en utilisant la librairie HIFOO 2.0 et testé sur le dispositif expérimental pour différents niveaux de remplissage. Finalement, le problème de la correction simultanée avec un correcteur HIFOO d'ordre réduit est aussi analysé
2 editions published in 2010 in English and held by 2 WorldCat member libraries worldwide
Cette thèse s'intéresse au problème du contrôle actif des vibrations structurelles d'une aile d'avion induites par le ballottement du carburant dans les réservoirs qu'elle contient. L'étude proposée ici est concentrée sur l'analyse d'un dispositif expérimental composé d'une longue plaque rectangulaire en aluminium équipée d'actionneurs et de capteurs piézoélectriques et d'un réservoir cylindrique. La difficulté principale réside dans le couplage complexe entre les modes de vibration de l'aile et les modes de ballottement du liquide. Un modèle de ce dispositif à l'aide d'équations aux dérivées partielles est tout d'abord construit. Ce modèle de dimension infinie couple une équation des plaques avec l'équation de Bernoulli pour le mouvement du fluide dans le réservoir. En analysant la contribution énergétique des modes, une approximation en dimension finie, de type espace d'état est alors construite. Après une méthode de recalage fréquentiel du modèle, un contrôle est réalisé en utilisant dans un premier temps une méthode par placement de pôle et dans un deuxième temps, la théorie de la commande robuste Hinfini. La dimension du modèle et les performances demandées imposent le calcul d'un contrôleur Hinfini d'ordre réduit, conçu en utilisant la librairie HIFOO 2.0 et testé sur le dispositif expérimental pour différents niveaux de remplissage. Finalement, le problème de la correction simultanée avec un correcteur HIFOO d'ordre réduit est aussi analysé
Eventbased control of networks modeled by a class of infinite dimensional systems by
Nicolás Espitia Hoyos(
)
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
Cette thèse propose des contributions sur la commande événementielle pour des réseaux modélisés par une classe des systèmes de dimension infinie. Premièrement nous nous focalisons sur la modélisation et contrôle frontière des réseaux qui sont décrits par des systèmes hyperboliques de lois de conservation. En nous inspirant de modèles macroscopiques dans le cadre des réseaux de communications, nous traitons des systèmes couplés EDPEDO, dont les noeuds (les serveurs) sont modélisés par des EDO nonlinéaires alors que des lignes de transmission sont décrites par des systèmes hyperboliques lorsque des retards peuvent être pris en compte. Pour le système linéarisé resultant, autour d'un point d'équilibre optimal, on effectue aussi bien une analyse de stabilité "Inputtostate stable" que de la synthèse du contrôle pour le gain asymptotique grâce à une analyse de fonction de Lyapunov et une formulation LMI.Ensuite, nous considérons des aspects théoriques de la commande évènementielle aux frontières pour les systèmes hyperboliques. D'un côté, avec cette stratégie de contrôle, nous ciblons la réduction de la consommation d' énergie en traitant les contraintes de communication et de calcul. D' autre part, nous utilisons cette stratégie comme une manière rigoureuse pour échantillonner temporellement lorsqu' on a besoin de mettre en oeuvre les contrôleurs continus sur une plateforme numérique. Une étude mathématique sur l'existence et l' unicité des solutions ainsi que sur les aspects de stabilité est réalisée
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
Cette thèse propose des contributions sur la commande événementielle pour des réseaux modélisés par une classe des systèmes de dimension infinie. Premièrement nous nous focalisons sur la modélisation et contrôle frontière des réseaux qui sont décrits par des systèmes hyperboliques de lois de conservation. En nous inspirant de modèles macroscopiques dans le cadre des réseaux de communications, nous traitons des systèmes couplés EDPEDO, dont les noeuds (les serveurs) sont modélisés par des EDO nonlinéaires alors que des lignes de transmission sont décrites par des systèmes hyperboliques lorsque des retards peuvent être pris en compte. Pour le système linéarisé resultant, autour d'un point d'équilibre optimal, on effectue aussi bien une analyse de stabilité "Inputtostate stable" que de la synthèse du contrôle pour le gain asymptotique grâce à une analyse de fonction de Lyapunov et une formulation LMI.Ensuite, nous considérons des aspects théoriques de la commande évènementielle aux frontières pour les systèmes hyperboliques. D'un côté, avec cette stratégie de contrôle, nous ciblons la réduction de la consommation d' énergie en traitant les contraintes de communication et de calcul. D' autre part, nous utilisons cette stratégie comme une manière rigoureuse pour échantillonner temporellement lorsqu' on a besoin de mettre en oeuvre les contrôleurs continus sur une plateforme numérique. Une étude mathématique sur l'existence et l' unicité des solutions ainsi que sur les aspects de stabilité est réalisée
Contributions à la stabilisation des systèmes à commutation affine by
Mathias Serieye(
Book
)
2 editions published in 2021 in English and held by 2 WorldCat member libraries worldwide
This thesis deals with the stabilization of switched affine systems with a periodic sampleddata switching control. The particularities of this class of nonlinear systems are first related to the fact that the control action is performed at the computation times by selecting the switching mode to be activated and, second, to the problem of providing an accurate characterization of the set where the solutions to the system converge to, i.e. the attractors. The contributions reported in this thesis have as common thread to reduce the conservatism made in the characterization of attractors, leading to guarantee the stabilization of the system at a limit cycle. After a brief introduction presenting the context and some main results, the first contributive chapter introduced a new method based on a new class of control Lyapunov functions that provides a more accurate characterization of the invariant set for a closedloop system. The contribution presented as a nonconvex optimization problem and referring to a LyapunovMetzler condition appears to be a preliminary result and the milestone of the forthcoming chapters. The second part deals with the stabilization of switched affine systems to limit cycles. After presenting some preliminaries on hybrid limit cycles and derived notions such as cycles in Chapter 3, stabilizing switching control laws are developed in Chapter 4. A control Lyapunov approach and a minswitching strategy are used to guarantee that the solutions to a nominal closedloop system converge to a limit cycle. The conditions of the theorem are expressed in terms of simple linear matrix inequalities (LMI), whose underlying necessary conditions relax the usual one in this literature. This method is then extended to the case of uncertain systems in Chapter 5, for which the notion of limit cycle needs to be adapted. Finally, the hybrid dynamical system framework is explored in Chapter 6 and the attractors are no longer characterized by possibly disjoint regions but as continuoustime closed and isolated trajectory. All along the dissertation, the theoretical results are evaluated on academic examples and demonstrate the potential of the method over the recent literature on this subject
2 editions published in 2021 in English and held by 2 WorldCat member libraries worldwide
This thesis deals with the stabilization of switched affine systems with a periodic sampleddata switching control. The particularities of this class of nonlinear systems are first related to the fact that the control action is performed at the computation times by selecting the switching mode to be activated and, second, to the problem of providing an accurate characterization of the set where the solutions to the system converge to, i.e. the attractors. The contributions reported in this thesis have as common thread to reduce the conservatism made in the characterization of attractors, leading to guarantee the stabilization of the system at a limit cycle. After a brief introduction presenting the context and some main results, the first contributive chapter introduced a new method based on a new class of control Lyapunov functions that provides a more accurate characterization of the invariant set for a closedloop system. The contribution presented as a nonconvex optimization problem and referring to a LyapunovMetzler condition appears to be a preliminary result and the milestone of the forthcoming chapters. The second part deals with the stabilization of switched affine systems to limit cycles. After presenting some preliminaries on hybrid limit cycles and derived notions such as cycles in Chapter 3, stabilizing switching control laws are developed in Chapter 4. A control Lyapunov approach and a minswitching strategy are used to guarantee that the solutions to a nominal closedloop system converge to a limit cycle. The conditions of the theorem are expressed in terms of simple linear matrix inequalities (LMI), whose underlying necessary conditions relax the usual one in this literature. This method is then extended to the case of uncertain systems in Chapter 5, for which the notion of limit cycle needs to be adapted. Finally, the hybrid dynamical system framework is explored in Chapter 6 and the attractors are no longer characterized by possibly disjoint regions but as continuoustime closed and isolated trajectory. All along the dissertation, the theoretical results are evaluated on academic examples and demonstrate the potential of the method over the recent literature on this subject
ISSLyapunov functions for timevarying hyperbolic systems of balance laws by
Christophe Prieur(
)
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
Global sensitivity analysis for the boundary control of an open channel by
Alexandre Janon(
)
1 edition published in 2015 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2015 in English and held by 2 WorldCat member libraries worldwide
Développement de stratégies de commandes pour des systèmes décrits par des équations aux dérivées partielles paraboliques
non linéaires by
Thérèse Azar(
)
1 edition published in 2021 in French and held by 2 WorldCat member libraries worldwide
The general context of the investigated study is the control of distributed parameter systems,such as those modeled by partial differential equations (PDE). The interest of this type of mathematical model compared to finite dimensions mathematical models is that it allows to consider the control of an infinity of dynamics at the same time. The fields of application are numerous and in the context of nuclear fusion for example, it isnecessary to determine control strategies for both zero stabilization and disturbances rejection. For nuclear fusion, the goal is to control the safety profile.The evolution of the spatial distribution of this key factor (conditioning the stability of the plasma) is described by a parabolic PDE system able to estimate the magnetic flux and the thermal state of the plasma. The problem of determining the control strategy to stabilize the safety profile is formulated as a minimization problem and solved using an inverse problem. Due to its wellknown illposed character, the method of regularization of the conjugate gradient is adapted to solve this inverse heat conduction problem. Implementation of quasionline strategies to obtain relevant controls for such nonlinear systems is developed. The actuators are intern to the geometry. The presented results show that this generalist numerical method makes it possible to obtain effective control strategies without strong assumptions on the studied system. The proposed alternative is meaningful if the mathematical model is in adequacy with the physical phenomena studied and as the system dynamics are not completely unknown
1 edition published in 2021 in French and held by 2 WorldCat member libraries worldwide
The general context of the investigated study is the control of distributed parameter systems,such as those modeled by partial differential equations (PDE). The interest of this type of mathematical model compared to finite dimensions mathematical models is that it allows to consider the control of an infinity of dynamics at the same time. The fields of application are numerous and in the context of nuclear fusion for example, it isnecessary to determine control strategies for both zero stabilization and disturbances rejection. For nuclear fusion, the goal is to control the safety profile.The evolution of the spatial distribution of this key factor (conditioning the stability of the plasma) is described by a parabolic PDE system able to estimate the magnetic flux and the thermal state of the plasma. The problem of determining the control strategy to stabilize the safety profile is formulated as a minimization problem and solved using an inverse problem. Due to its wellknown illposed character, the method of regularization of the conjugate gradient is adapted to solve this inverse heat conduction problem. Implementation of quasionline strategies to obtain relevant controls for such nonlinear systems is developed. The actuators are intern to the geometry. The presented results show that this generalist numerical method makes it possible to obtain effective control strategies without strong assumptions on the studied system. The proposed alternative is meaningful if the mathematical model is in adequacy with the physical phenomena studied and as the system dynamics are not completely unknown
Table alphabétique des mariages de la paroisse d'Auxerre (SaintPierreenVallée) : 16391792 by
Christophe Prieur(
Book
)
1 edition published in 1986 in French and held by 2 WorldCat member libraries worldwide
1 edition published in 1986 in French and held by 2 WorldCat member libraries worldwide
Collaborative sourceseeking control by
Ruggero Fabbiano(
)
1 edition published in 2015 in English and held by 2 WorldCat member libraries worldwide
The dissertation faces the problem of source localisation, a topic which has been extensively studied in recent literature due to its large number of applications. In particular, it focuses on steering multiple sensors, able to take pointwise measurements of the emitted quantity, towards the source without making use of any position information, which happens to be unavailable in many practical cases (for example, underwater or underground exploration). By making some assumptions on the diffusion process, we develop a model which allows us to use some mathematical tools (the Poisson integral and its derivatives) for a simple approximation of the gradient of the function describing the diffusion process, whose source represents its maximum, making it possible to perform a gradient ascent to find the source location. The contributions are threefold: first, we use such tools to solve a 2dimensional centralised sourceseeking problem, where a single vehicle, equipped with multiple sensors and without position information, is moving in a planar environment where a source is supposed to emit. Then, we extend it to a 3dimensional framework, considering a flying vehicle equipped with sensors moving in the space; for this more general case, in addition to simulation validation, we provide a theoretical study of the convergence properties of the proposed control law. Finally, we tackle the distributed sourcelocalisation problem, considering several autonomous moving sensors (in two dimensions); in addition to the problem of implementing the sourcelocalisation algorithm in a distributed manner, in this latter case we have also to guarantee a suitable formation control, to ensure the correctness of the gradient estimation and hence reach the source
1 edition published in 2015 in English and held by 2 WorldCat member libraries worldwide
The dissertation faces the problem of source localisation, a topic which has been extensively studied in recent literature due to its large number of applications. In particular, it focuses on steering multiple sensors, able to take pointwise measurements of the emitted quantity, towards the source without making use of any position information, which happens to be unavailable in many practical cases (for example, underwater or underground exploration). By making some assumptions on the diffusion process, we develop a model which allows us to use some mathematical tools (the Poisson integral and its derivatives) for a simple approximation of the gradient of the function describing the diffusion process, whose source represents its maximum, making it possible to perform a gradient ascent to find the source location. The contributions are threefold: first, we use such tools to solve a 2dimensional centralised sourceseeking problem, where a single vehicle, equipped with multiple sensors and without position information, is moving in a planar environment where a source is supposed to emit. Then, we extend it to a 3dimensional framework, considering a flying vehicle equipped with sensors moving in the space; for this more general case, in addition to simulation validation, we provide a theoretical study of the convergence properties of the proposed control law. Finally, we tackle the distributed sourcelocalisation problem, considering several autonomous moving sensors (in two dimensions); in addition to the problem of implementing the sourcelocalisation algorithm in a distributed manner, in this latter case we have also to guarantee a suitable formation control, to ensure the correctness of the gradient estimation and hence reach the source
Modelling and stability analysis of flexible robots : a distributed parameter portHamiltonian approach by
Andrea Mattioni(
)
2 editions published in 2021 in English and held by 2 WorldCat member libraries worldwide
The objective of this thesis is to provide a mathematical framework that allows to explicit the dynamical model of a class of flexible mechanisms, to design their control law and to analyze the resulting closed loop asymptotic behaviour. From a mathematical point of view, the flexible parts are distributed parameter systems whose dynamics are described by Partial Differential Equations (PDE), while the dynamics of the rigid parts are described by Ordinary Differential Equation (ODE). Therefore, the total model is described by a mixed set of ODEPDE (mPDEODE). For studying these dynamic models, this thesis uses the portHamiltonian framework combined with the infinitedimensional semigroup theory.First, we define a rigorous procedure based on the Least Action Principle for deriving the model of mechanisms with possible flexible components, providing several illustrative examples. The general class of nonlinear systems enclosing all the proposed examples is shown to be passive with respect to its mechanical energy. In this class of systems, the distributed parameter parts are modelled as one dimensional boundary control systems.Second, we restrict ourselves to a linear class of mODEPDE systems for which we propose different control laws. We show that the proposed control laws allow achieving asymptotic or exponential stability.Finally, a rotating arm that enters in contact with the external environment is studied in case the link is considered as being both rigid or flexible. Since this system exhibits instant changes in the impact times, we study this problem with the help of switching theory applied to infinite dimensional systems
2 editions published in 2021 in English and held by 2 WorldCat member libraries worldwide
The objective of this thesis is to provide a mathematical framework that allows to explicit the dynamical model of a class of flexible mechanisms, to design their control law and to analyze the resulting closed loop asymptotic behaviour. From a mathematical point of view, the flexible parts are distributed parameter systems whose dynamics are described by Partial Differential Equations (PDE), while the dynamics of the rigid parts are described by Ordinary Differential Equation (ODE). Therefore, the total model is described by a mixed set of ODEPDE (mPDEODE). For studying these dynamic models, this thesis uses the portHamiltonian framework combined with the infinitedimensional semigroup theory.First, we define a rigorous procedure based on the Least Action Principle for deriving the model of mechanisms with possible flexible components, providing several illustrative examples. The general class of nonlinear systems enclosing all the proposed examples is shown to be passive with respect to its mechanical energy. In this class of systems, the distributed parameter parts are modelled as one dimensional boundary control systems.Second, we restrict ourselves to a linear class of mODEPDE systems for which we propose different control laws. We show that the proposed control laws allow achieving asymptotic or exponential stability.Finally, a rotating arm that enters in contact with the external environment is studied in case the link is considered as being both rigid or flexible. Since this system exhibits instant changes in the impact times, we study this problem with the help of switching theory applied to infinite dimensional systems
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Related Identities
 Argomedo, Federico Bribiesca Opponent Author
 Witrant, Emmanuel Thesis advisor
 Astolfi, A. (Alessandro) Editor
 Jiang, Z.P (ZhongPing) Author Editor
 Praly, Laurent Honoree
 École doctorale électronique, électrotechnique, automatique, traitement du signal (Grenoble) Other
 Grenoble Images parole signal automatique Other
 Communauté d'universités et d'établissements Université Grenoble Alpes Degree grantor
 Tarbouriech, Sophie (19......). Other Thesis advisor
 SpringerLink (Online service) Other
Associated Subjects
Adaptive control systems Automatic control Automatic controlComputer simulation Big dataSocial aspects Data miningSocial aspects Engineering Feedback control systems Game theory Linear control systems Linear time invariant systems Mechatronics Nonlinear control theory Nuclear fusion Robotics Statistics System theory TokamaksSafety measures