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Proposition de lois de commande pour la stabilisation de modèles flous

Abstract : For several years, the stability analysis of a closed loop including a fuzzy controller has been studied. Especially with the state space approach, the stability analysis is concerned with a Takagi-Sugeno-Kang fuzzy models. This analysis can be done using several methods, for example, Lyapunov approach, equivalence with switching systems, taking into account a fuzzy model as a linear one with uncertainties ... A classical way to find a fuzzy control law is the use of a Parallel Distributed Compensation (PDC). This one remains in local state feedback laws for each rule of the controller and the stability analysis is done with a Lyapunov approach. This work presents control laws, mainly. for continuous fuzzy models of Takagi-Sugeno-Kang which are not directly put in a PDC form. A first approach is related to the work on simultaneous quadratic stabilization of a family of linear SIMO systems. Sufficient conditions to derive a stabilizing control law for TSK SIMO continuous fuzzy systems are given and a separation principle is also provided with a fuzzy observer. A second approach based on a particular family of MIMO TSK fuzzy models allows to reduce the conservatism of results found in the litterature and a separation principle is also given in these cases. For MIMO TSK fuzzy models we also give sufficient conditions of stabilization using optimal control tools. All stability approaches studied can be converted into convex optimization problems over Linear Matrix lnequalities (LMls) constraints. These optimization problems can be solved with efficient algorithms. At last, two real-time applications are treated. The first one is concemed with electrical vehicle control, and the second is the well-known inverted pendulum system.
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  • HAL Id : tel-03461742, version 1

Citation

Laurent Vermeiren. Proposition de lois de commande pour la stabilisation de modèles flous. Automatique / Robotique. Université de Valenciennes et du Hainaut-Cambrésis, 1998. Français. ⟨NNT : 1998VALE0024⟩. ⟨tel-03461742⟩

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