Control theory and dynamical systems

Abstract : This thesis is devided into three parts. In the first part we begin by describing some well known results in geometric control theory such as the Chow Rashevsky Theorem, the Kalman rank condition, the End-Point Mapping and the linear test. Moreover, we define and study briefly local controllability around a reference control at first and second order. In the second part we provide an elementary proof of the Franks lemma for geodesic flows using basic tools of geometric control theory. In the last part, given a compact Riemannian manifold, we prove a uniform Franks' lemma at second order for geodesic flows and apply the result in persistence theory. In this part we introduce with more details notions of local controllability at first and second order. In fact, we provide a second order controllability result whose proof is long and technical.
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Ayadi Lazrag. Control theory and dynamical systems. General Mathematics [math.GM]. Université Nice Sophia Antipolis, 2014. English. ⟨NNT : 2014NICE4060⟩. ⟨tel-01080164⟩

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