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                <title xml:lang="en">Computational Approaches to Analysis and Control of Hybrid Systems</title>
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                <term xml:lang="en">Hybrid dynamical systems</term>
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                <term xml:lang="fr">Systèmes dynamiques hybrides</term>
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              <p>A hybrid system is a dynamical system exhibiting both continuous and discrete behaviors. Motivated by the multiplication of ''discrete'' embedded computing devices interacting with the ''continuous'' physical world, the research on hybrid systems has rapidly developed since the nineties at the intersection of computer science, control theory and applied mathematics. This thesis presents our theoretical and methodological contributions to this field. In a first part, we introduce an approximation framework that applies to dynamical systems that can be continuous, discrete or hybrid; applications, including some in the field of symbolic control, are presented. The second part deals with reachability analysis, a computational technique which is very useful for the analysis of hybrid systems. Finally, the third part presents our contributions to multi-agent dynamical systems.</p>
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              <p>Un système hybride est un système dynamique exhibant à la fois des comportements de nature discrète et continue. Motivée par la multiplication de composants informatiques embarqués ''discrets'' interagissant avec le monde physique ''continu'', la recherche sur les systèmes hybrides s'est développée rapidement depuis les années 90 à l'intersection de l'informatique, de l'automatique et des mathématiques appliquées. Ce mémoire présente nos contributions, théoriques ou méthodologiques, à ce domaine. Dans une première partie, nous introduisons un cadre d'approximation qui s'applique aux systèmes dynamiques continus, discrets et hybrides; des applications, notamment dans le domaine du contrôle symbolique sont présentées. La deuxième partie est consacrée à l'analyse d'atteignabilité, une technique computationnelle très utile pour l'analyse des systèmes hybrides. Enfin, la troisième partie porte sur les systèmes dynamiques multi-agents.</p>
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