Networked control: taking into account sample period variations and actuators saturation

International audienceThis paper exposes a novel method to cope with the stabilization of networked control systems with asynchronous sampling and actuators saturations. The constructive stabilization criterion is expressed in terms of linear matrices inequalities using the continuous-time model of the systems. However the stability analysis of the closed-loop system is based on the discrete-time Lyapunov Theorem. An example shows that the conservatism of the conditions has been reduced with respect to the literature

Stabilization of Neutral Systems with Saturating Control Inputs

International audienceThis paper focuses on the stabilization problem of neutral systems in the presence of time-varying delays and control saturation. Based on a descriptor approach and the use of a modified sector relation, global and local stabilization conditions are derived using Lyapunov-Krasovskii functionals. These conditions, formulated directly as linear matrix inequalities (LMIs), allow to relate the control law to be computed to a set of admissible initial conditions, for which the asymptotic and exponential stabilities of the closed-loop system are ensured. An extension of these conditions to the particular case of retarded systems is also provided. From the theoretical conditions, optimization problems with LMI constraints are therefore proposed to compute stabilizing state feedback gains with the aim of ensuring stability for a given set of admissible initial conditions or the global stability of the closed-loop system. A numerical example illustrates the application of the proposed results

Semi-active suspension control problem: some new results using an LPV /H ∞ state feedback input constrained control

International audience— The semi-active suspension control problem faces the challenge of the dissipativity constraints of the semi-active dampers. This induces some compromises (actuator saturation, comfort, road holding...) which need to be taken into account in the control design step. In this paper, a state feedback input constrained control problem for LPV systems is considered with H ∞ performance objective. Stabilization conditions based on the Finsler's Lemma are derived in order to ensure the stability in the presence of the input saturation, and to attenuate the disturbance effects. To this aim, two different Lyapunov functions are used. For the stability analysis, a generalized sector condition for LPV systems is applied to treat the nonlinearity caused by the actuator saturation. The considered performance objective regards the reduction of L 2 gain from the disturbance to the controlled output. The LPV controller is computed from the solution of LMIs considering a polytopic representation for the LPV closed-loop system. These theoretical results are applied to a semi-active suspension system where the dissipativity conditions of the semi-active dampers are recast as saturation conditions on the control inputs. The comfort criteria is used as a performance objective in this study. Some simulation results are presented in order to illustrate the effectiveness of the proposed approach

Static anti-windup synthesis for linear systems with time-varying input delays

International audienceThis article considers the design of an anti-windup compensator for linear systems subject to time-varying input delays and saturating actuators. Local and global stabilization conditions ensuring both external as well as internal stability of the closed-loop system are derived directly as linear matrix inequalities (LMIs). To compute the anti-windup gains, these conditions are cast into the following optimization problems: maximization of the set of admissible initial conditions, maximization of the bound of admissible L2 disturbances or the maximization of the L2-gain from the disturbance to the regulated output. Simulation examples are provided to illustrate the proposed solution

Sur la stabilité locale de systèmes linéaires avec saturation des commandes

The aim of this thesis is the study of the local asymptotic stability of discrete-time linear systems subject to control saturation. The work is developed by using two representations of the closed-loop saturated system, namely by regions of saturation and by polytopic model. The analysis of the stability of the closed-loop saturated system as well as the synthesis of saturating control laws are based on the concept of contractive sets. In this context, new results are proposed by considering two distinct approaches. The first one deals with polyhedral sets. The contractivity of the trajectories of the saturated system in polyhedral sets is studied. By considering the representation by regions of saturation, necessary and sufficient conditions are stated for the polyhedral contractivity with respect to the trajectories of the saturated system. From the representation by polytopic model only sufficient conditions are stated. The conditions obtained with both approaches lead to the formulation of algorithms to determine polyhedral domains of asymptotic stability and non-linear behavior for the closed-loop system. These algorithms are based on linear programming. The second approach deals with ellipsoidal sets and considers the polytopic representation of the saturated system. A sufficient condition for the contractivity of ellipsoids with respect to the trajectories of the closed-loop system are formulated in terms of linear matrix inequalities (LMIs). From this condition, an algorithm to compute approximations of the basin of attraction of the origin of the closed-loop system is proposed. This algorithm is based on the solution of convex optimization problems. On the other hand, given a set of initial admissible conditions X0, an LMI-based framework is proposed to compute saturating control laws that ensure the asymptotic convergence to the origin of all the trajectories emanating from X0.Cette thèse a pour but l'étude de la stabilité asymptotique locale des systèmes linéaires à temps discret dont les commandes sont soumises à des saturations. L'étude est développée à partir de deux représentations du système saturé en boucle fermée : par régions de saturation et par modèle polytopique. L'analyse de la stabilité du système saturé en boucle fermée ainsi que la synthèse de la loi de commande saturante avec l'objectif de garantir la stabilité d'un domaine d'états admissibles, sont basées sur le concept d'ensembles contractifs. Dans ce contexte, des résultats sont obtenus en considérant deux approches distinctes. La première approche considère des ensembles polyédraux. Des conditions pour la contractivité des trajectoires du système en boucle fermée dans un polyèdre sont étudiées : d'une part, des conditions nécessaires et suffisantes sont établies à partir de la représentation par régions de saturation et, d'autre part, des conditions suffisantes sont obtenues à partir de la représentation par modèle polytopique. Ces conditions permettent de formuler des algorithmes, basés sur des schémas de programmation linéaire, ayant pour objectif la détermination de régions polyédrales où la stabilité asymptotique locale du système en boucle fermée est garantie même si la commande sature. La deuxième approche considère des ensembles ellipsoïdaux et la représentation polytopique du système saturé. Des conditions suffisantes pour la contractivité d'ellipsoïdes par rapport au système saturé sont établies sous la forme d'inégalités matricielles linéaires (LMIs). A partir de ces conditions, un algorithme basé sur des schémas d'optimisation convexe est proposé pour la détermination d'approximations de la région d'attraction de l'origine à travers des ellipsoïdes contractifs. D'autre part, pour un ensemble donné de conditions initiales X0, des conditions sont formulées, également sous la forme de L MIs, pour permettre la détermination d'une loi de commande saturante garantissant la stabilité asymptotique vers l'origine de toutes les trajectoires initialisées dans X0

Taking into account period variations and actuators saturation in sampled-data systems

International audienceThis paper deals with the problem of stability and stabilization of sampled-data systems under asynchronous samplings and actuators saturation. The method is based, on the first hand, on the use of a novel class of Lyapunov functionals whose derivative is negative along the trajectories of the continuous-time model of the sampled data system. It is shown that this fact guarantees that a quadratic Lyapunov function is strictly decreasing for the discrete-time asynchronous system. On the other side, the control saturation is taken into account from the use of a modified sector condition. These ingredients lead to the formulation of improved LMI conditions that can be cast in optimization problems aiming at enlarging estimates of the region of attraction of the closed-loop system or maximizing the bounds on the sampling period jitter for which stability and stabilization are ensured

Well-posedness and stability of a 1D wave equation with saturating distributed input

International audienceIn this paper, it is considered a wave equation with a one-dimensional space variable, which describes the dynamics of string deflection. The slope has a finite length and is attached at both boundaries. It is equipped with a distributed actuator subject to a saturation. By closing the loop with a saturating input proportional to the speed of the deformation, it is thus obtained a nonlinear partial differential equation, which is the generalization of the classical 1D wave equation. The well-posedness is proven by using nonlinear semigroups technics. The asymptotic stability of the closed-loop system, when the tuning parameter has a suitable sign, is proven by Lyapunov technics and a sector condition describing the saturating input

Stability Analysis of Dynamic Output Controllers under Aperiodic Sampling and Input Saturation

International audienceThis paper addresses stability issues of sampled-data controllers. Considering a continuous-time linear plant and a linear discrete-time dynamic output feedback control law designed from a classical periodic sampling paradigm, the main goal is to assess the effects of aperiodic sampling on the closed-loop stability. This aperiodic sampling models for instance the communication delays and package losses through a network. In addition, the effects of control signal saturation on the stability and the maximal admissible sampling interval are also taken into account . In this context, based on the use of a looped functional, linear matrix inequalities (LMI) are derived to ensure the global asymptotic stability of the origin for the aperiodic sampled-data closed-loop system, provided a bound on the maximal sampling interval is given. An optimization problem in order to evaluate the maximal admissible value for the interval between two sampling instants is then associated to the LMI conditions

Control Design for LPV Systems with Input Saturation and State Constraints: an Application to a Semi-Active Suspension

International audienceThis paper proposes a control design strategy for LPV systems subject to additive disturbances in the presence of actuator saturation and state constraints. LMI conditions are derived in order to simultaneously compute an LPV controller and an anti-windup gain that ensures the boundedness of the trajectories, considering that the disturbances belong to a given admissible set. The disturbance attenuation is addressed via an H¥ constraint. Besides, state constraints (corresponding to the local validity of the LPV model and system structural limits) are always assured. The theoretical results are applied to a quarter-car model rewritten in the LPV framework where the passivity constraint is recast to the saturation one. The interest of the provided methodology is emphasized by simulations

Stabilization of Neutral Systems with Saturating Control Inputs

International audienceThis paper focuses on the stabilization problem of neutral systems in the presence of time-varying delays and control saturation. Based on a descriptor approach and the use of a modified sector relation, global and local stabilization conditions are derived using Lyapunov-Krasovskii functionals. These conditions, formulated directly as linear matrix inequalities (LMIs), allow to relate the control law to be computed to a set of admissible initial conditions, for which the asymptotic and exponential stabilities of the closed-loop system are ensured. An extension of these conditions to the particular case of retarded systems is also provided. From the theoretical conditions, optimization problems with LMI constraints are therefore proposed to compute stabilizing state feedback gains with the aim of ensuring stability for a given set of admissible initial conditions or the global stability of the closed-loop system. A numerical example illustrates the application of the proposed results