Sur la structure de l’ensemble d’accessibilité de certains systèmes: Application à l’equivalence des systèmes. (On the structure of the accessibility set of certain systems: Application to the equivalence of systems). (French) Zbl 0574.49023

The topological properties of accessibility sets for a large class of nonlinear systems are investigated. In particular, it is shown that accessible sets of self-invariant systems have a simple topological structure (the interior and the interior of the closure coincide). As a consequence, systems which are equivalent (in an appropriate sense) have accessible sets with the same interior and the same boundary. This is used to prove a conjecture by L. R. Hunt.
Reviewer: A.Bacciotti


93B03 Attainable sets, reachability
93B05 Controllability
93C10 Nonlinear systems in control theory
57R27 Controllability of vector fields on \(C^\infty\) and real-analytic manifolds
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