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.
CITATION STYLE
Boscain, U., & Sigalotti, M. (2019). Introduction to controllability of nonlinear systems. In Springer INdAM Series (Vol. 33, pp. 203–219). Springer International Publishing. https://doi.org/10.1007/978-3-030-18921-1_4
Mendeley helps you to discover research relevant for your work.