Introduction to controllability of non-linear systems

Ugo Boscain (1, 2, 3) , Mario Sigalotti (2, 3)

1 CNRS - Centre National de la Recherche Scientifique
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
3 CaGE - Control And GEometry

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.

Domaines: Optimisation et contrôle [math.OC]

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⟩