robust stabilization using a sampled-data strategy of uncertain neutral state-delayed systems subject to input limitations

Producción CientíficaStabilization of neutral systems with state delay is considered in the presence of uncertainty and input limitations in magnitude. The proposed solution is based on simultaneously characterizing a set of stabilizing controllers and the associated admissible initial conditions through the use of a free weighting matrix approach. From this mathematical characterization, state feedback gains that ensure a large set of admissible initial conditions are calculated by solving an optimization problem with LMI constraints. Some examples are presented to compare the results with previous approaches in the literature.MICINnn DPI2014-54530-

Vehicle Stability Control Considering the Driver-in-the-Loop

A driver‐in‐the‐loop modeling framework is essential for a full analysis of vehicle stability systems. In theory, knowing the vehicle’s desired path (driver’s intention), the problem is reduced to a standard control system in which one can use different methods to produce a (sub) optimal solution. In practice, however, estimation of a driver’s desired path is a challenging – if not impossible – task. In this thesis, a new formulation of the problem that integrates the driver and the vehicle model is proposed to improve vehicle performance without using additional information from the future intention of the driver. The driver’s handling technique is modeled as a general function of the road preview information as well as the dynamic states of the vehicle. In order to cover a variety of driving styles, the time‐ varying cumulative driver's delay and model uncertainties are included in the formulation. Given that for practical implementations, the driver’s future road preview data is not accessible, this information is modeled as bounded uncertainties. Subsequently, a state feedback controller is designed to counteract the negative effects of a driver’s lag while makes the system robust to modeling and process uncertainties. The vehicle’s performance is improved by redesigning the controller to consider a parameter varying model of the driver‐vehicle system. An LPV controller robust to unknown time‐varying delay is designed and the disturbance attenuation of the closed loop system is estimated. An approach is constructed to identify the time‐varying parameters of the driver model using past driving information. The obtained gains are clustered into several modes and the transition probability of switching between different driving‐styles (modes) is calculated. Based on this analysis, the driver‐vehicle system is modeled as a Markovian jump dynamical system. Moreover, a complementary analysis is performed on the convergence properties of the mode‐dependent controller and a tighter estimation for the maximum level of disturbance rejection of the LPV controller is obtained. In addition, the effect of a driver’s skills in controlling the vehicle while the tires are saturated is analyzed. A guideline for analysis of the nonlinear system performance with consideration to the driver’s skills is suggested. Nonlinear controller design techniques are employed to attenuate the undesirable effects of both model uncertainties and tire saturation

Contributions à la stabilisation des systèmes à commutation affine

Cette thèse porte sur la stabilisation des systèmes à commutation dont la commande, le signal de commutation, est échantillonné de manière périodique. Les difficultés liées à cette classe de systèmes non linéaires sont d'abord dues au fait que l'action de contrôle est effectuée aux instants de calcul en sélectionnant le mode de commutation à activer et, ensuite, au problème de fournir une caractérisation précise de l'ensemble vers lequel convergent les solutions du système, c'est-à-dire l'attracteur. Dans cette thèse, les contributions ont pour fil conducteur la réduction du conservatisme fait pendant la définition d'attracteurs, ce qui a mené à garantir la stabilisation du système à un cycle limite. Après une introduction générale où sont présentés le contexte et les principaux résultats de la littérature, le premier chapitre contributif introduit une nouvelle méthode basée sur une nouvelle classe de fonctions de Lyapunov contrôlées qui fournit une caractérisation plus précise des ensembles invariants pour les systèmes en boucle fermée. La contribution présentée comme un problème d'optimisation non convexe et faisant référence à une condition de Lyapunov-Metzler apparaît comme un résultat préliminaire et une étape clé pour les chapitres à suivre. La deuxième partie traite de la stabilisation des systèmes affines commutés vers des cycles limites. Après avoir présenté quelques préliminaires sur les cycles limites hybrides et les notions dérivées telles que les cycles au Chapitre 3, les lois de commutation stabilisantes sont introduites dans le Chapitre 4. Une approche par fonctions de Lyapunov contrôlées et une stratégie de min-switching sont utilisées pour garantir que les solutions du système nominal en boucle fermée convergent vers un cycle limite. Les conditions du théorème sont exprimées en termes d'Inégalités Matricielles Linéaires (dont l'abréviation anglaise est LMI) simples, dont les conditions nécessaires sous-jacentes relâchent les conditions habituelles dans cette littérature. Cette méthode est étendue au cas des systèmes incertains dans le Chapitre 5, pour lesquels la notion de cycles limites doit être adaptée. Enfin, le cas des systèmes dynamiques hybrides est exploré au Chapitre 6 et les attracteurs ne sont plus caractérisés par des régions éventuellement disjointes mais par des trajectoires fermées et isolées en temps continu. Tout au long de la thèse, les résultats théoriques sont évalués sur des exemples académiques et démontrent le potentiel de la méthode par rapport à la littérature récente sur le sujet.This thesis deals with the stabilization of switched affine systems with a periodic sampled-data 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 closed-loop system. The contribution presented as a nonconvex optimization problem and referring to a Lyapunov-Metzler 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 min-switching strategy are used to guarantee that the solutions to a nominal closed-loop 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 continuous-time 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