Invariant measures and controllability of finite systems on compact manifolds

Philippe Jouan (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the Equivalence Theorem of \cite{Jouan09} and of the existence of an invariant measure on certain compact homogeneous spaces.

Mots clés: Compact homogeneous spaces; Linear systems; Controllability; Finite dimensional Lie algebras; Haar measure

Domaines: Optimisation et contrôle [math.OC]

Philippe Jouan. Invariant measures and controllability of finite systems on compact manifolds. 2010. ⟨hal-00541485⟩