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Introduction to controllability of non-linear systems

Abstract : We present some basic facts about the controllability of nonlinear finite dimensional systems. We introduce the concepts of Lie bracket and of Lie algebra generated by a family of vector fields. We then prove the Krener theorem on local accessibility and the Chow-Rashevskii theorem on controllability of symmetric systems. We then introduce the theory of compatible vector fields and we apply it to study control-affine systems with a recurrent drift or satisfying the strong Lie bracket generating assumption. We conclude with a general discussion about the orbit theorem by Sussmann and Nagano.
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Ugo Boscain, Mario Sigalotti. Introduction to controllability of non-linear systems. Serena Dipierro. Contemporary Research in Elliptic PDEs and Related Topics, Springer, 2019, ⟨10.1007/978-3-030-18921-1_4⟩. ⟨hal-02421207⟩

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