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Algorithmes hybrides pour le contrôle optimal des systèmes non linéaires

Abstract : This thesis is devoted to the analysis of non linear control problems by hybrid computation methods. We defend the idea that the use of hybrid systems allows the approximate resolution of non linear control problems without any a priori knowledge of the behavior of the considered systems. In the first part we focus on the modelling of non linear control systems by a new class of piecewise affine hybrid systems. Particularly, we propose a full analysis of the error and of the convergence of the hybrid approximation. The second part deals with the controllability to the origin of non linear systems. We first provide an analysis of the approximation error between the non linear controllable domain and its hybrid approximation. We then propose a constructive approach for the computation of the controllable domain which allows to reduce the exploration of the discrete states of the hybrid automaton. The last part is devoted to the search of optimal solutions of the non linear and hybrid optimal control problems. We first justify the relevance of our hybrid model thanks to two approaches: the Pontryagin maximum principle and viscosity solutions of Hamilton-Jacobi-Bellman equations. Particularly, we state a hybrid maximum principle which provides us the structure of the hybrid optimal control. These three parts answer to the main purpose : to develop by the hybrid computation combining numerical analysis and computer algebra, some mathematical and algorithmic efficient tools for the analysis of non linear control systems.
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Submitted on : Tuesday, November 7, 2006 - 5:19:01 PM
Last modification on : Wednesday, July 28, 2021 - 3:56:54 AM
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  • HAL Id : tel-00112203, version 1



Aude Rondepierre. Algorithmes hybrides pour le contrôle optimal des systèmes non linéaires. Mathématiques [math]. Institut National Polytechnique de Grenoble - INPG, 2006. Français. ⟨tel-00112203⟩



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