Analyse Algorithmique des Systèmes Hybrides

Abstract : This thesis is devoted to the algorithmic analysis of hybrid systems. We consider several problems linked to the study and the control of piecewise linear hybrid systems. In the first part, we introduce the fundamental notions of the theory. These are illustrated by numerous examples. The second part is devoted to the computation of the executions accepted by a hybrid system. A method for event detection is proposed. The case of periodic executions is also examinated. In the third part, we consider the problem which consists in computing the reachable set of a hybrid system. Particularly, we propose a method for the systems where the continuous dynamics are given by uncertain differential equations. In the fourth part, we propose an approach for the control of hybrid systems. We construct a multiresolution analysis of the set of inputs of a linear system and compute an associated set of wavelets. The properties of this basis are interesting for the synthesis of input signals of a hybrid system. In the last part, we show that the methods developped for piecewise linear hybrid systems can be used to analyse non-linear dynamical systems.
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Submitted on : Friday, October 8, 2004 - 10:55:46 AM
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Antoine Girard. Analyse Algorithmique des Systèmes Hybrides. Modélisation et simulation. Institut National Polytechnique de Grenoble - INPG, 2004. Français. ⟨tel-00007064⟩

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