Calculus of Variations and Geometric Measure Theory
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U. Boscain - D. Cannarsa - V. Franceschi - M. Sigalotti

Local controllability does imply global controllability

created by franceschi on 14 Oct 2021
modified on 27 Oct 2021



Inserted: 14 oct 2021
Last Updated: 27 oct 2021

Year: 2021

ArXiv: 2110.06631 PDF


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. Quite surprisingly, the question of whether local controllability implies global controllability seems not to have been considered in the literature. We show in this paper that a control system satisfying local controllability is controllable.

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