Introduction to controllability of nonlinear systems (Q2009099)

The authors present some basic facts about the controllability of nonlinear finite dimensional systems. The concepts of Lie bracket and of Lie algebra generated by a family of vector fields are introduced. The Krener theorem on local accessibility and the Chow-Rashevskii theorem on controllability of symmetric Systems is proven. The theory of compatible vector fields is introduced and applied to study control-affine systems with a recurrent drift or satisfying the strong Lie bracket generating assumption. Finally, a general discussion about the orbit theorem by Sussmann and Naganois is given. For the entire collection see [Zbl 1419.35002].