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Deux Méthodes d'Approximation pour un Contrôle Optimal Semi-Décentralisé pour des Systèmes Distribués

Abstract : In this thesis, we have developed two approaches to build semi-decentralized approached controllers. The thesis is divided into two distinct parts, each one dealing with its own specific method. First Part: it deals with semi-decentralized approximation of an optimal control for partial derivative equations in a bounded domain. In this part, we outline an optimal control computation method for linear distributed systems, with a bounded or not bounded input operator. Its construction depends on the functional computation of self adjoint operators and on Dunford-Schwartz formula. It is suited to computation architectures with very thin granularity and semi-decentralized coordination. Finally, it is illustrated by examples dealing especially with the internal stabilization of heat, of vibrations in a beam or even in a micro-cantilevers array ... Second Part: we deal with derivation of state-realizations of linear operators solutions to some operatorial linear differential equations in one-dimensional bounded domains. We have developed two approaches in the framework of diffusive realizations. One is with regular symbols and the other is with symbols singular on the real axis. Then, we have illustrated the theories and we have developed numerical methods in the context of an application to a Lyapunov equation issued from the optimal control theory for the heat equation. A practical interest of this approach is for real-time computation on processors with semi-decentralized architecture.
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Submitted on : Tuesday, February 15, 2011 - 2:01:31 AM
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  • HAL Id : tel-00565898, version 1

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Youssef Yakoubi. Deux Méthodes d'Approximation pour un Contrôle Optimal Semi-Décentralisé pour des Systèmes Distribués. Mathématiques [math]. Université de Franche-Comté, 2010. Français. ⟨tel-00565898⟩

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