Local controllability does imply global controllability
Ugo Boscain, Daniele Cannarsa, Valentina Franceschi, and Mario, Sigalotti
TL;DR
This paper proves that local controllability of a control system guarantees its global controllability, providing an alternative proof to previous results.
Contribution
It offers a self-contained proof that local controllability implies global controllability, simplifying prior approaches.
Findings
Local controllability implies global controllability
Provides an alternative proof to previous results
Simplifies understanding of control system properties
Abstract
We say that a control system is locally controllable if the attainable set from any state contains an open neighborhood of , 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.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Stability and Control of Uncertain Systems · Advanced Differential Equations and Dynamical Systems