Local controllability does imply global controllability

Abstract

We say that a control system is locally controllable if the attainable set from any state x contains an open neighborhood of x, while it is controllable if the attainable set from any state is the entire state manifold. We show in this note that a control system satisfying local controllability is controllable. Our self-contained proof is alternative to the combination of two previous results by Kevin Grasse.

Publication
In ArXiv eprint
Daniele Cannarsa
Daniele Cannarsa
Postdoctoral Researcher in Mathematics

My research interests include sub-Riemannian geometry and geometric control theory