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Analyse et optimisation d'une classe de systèmes dynamiques hybrides à commutations autonomes

Abstract : This work is devoted to the study of a particular class of hybrid dynamical systems (h.d.s.) with autonomous switchings, these being generated by a hysteresis phenomenon. More particularly, after having introduced the studied mathematical model, an analysis of this h.d.s. class is realized with notably a study of limit cycles (equations to determine them, stability) and of bifurcations (saddle node, period doubling). Existence of some properties which characterize chaotic systems like the sensitivity to initial conditions is also highlighted with both graphic and computationl (Lyapunov exponent) ways. Finally, a parametric optimization part is proposed in order to improve some system performances. All those theoretical results are applied to a thermal system (thermostat with an anticipative resistance) and to an electronic one (DC/DC converter) with formal calculus (Maple), interval analysis (Proj2D) and numerical simulations (Matlab).
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https://tel.archives-ouvertes.fr/tel-00464057
Contributor : Céline Quemard <>
Submitted on : Monday, March 15, 2010 - 5:58:26 PM
Last modification on : Monday, March 21, 2016 - 5:35:24 PM
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Céline Quemard. Analyse et optimisation d'une classe de systèmes dynamiques hybrides à commutations autonomes. Mathématiques [math]. Université d'Angers, 2007. Français. ⟨tel-00464057⟩

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