Controllability of Linear Systems on Lie Groups

Philippe Jouan (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

A vector field on a connected Lie group is said to be linear if its flow is a one parameter group of automorphisms. A control-affine system is linear if the drift is linear and the controlled vector fields right invariant. The controllability properties of such systems are studied, mainly in the case where the derivation of the group Lie algebra that can be associated to the linear vector field is inner. After some general considerations controllability properties on semi simple, nilpotent and compact Lie groups are stated. The paper ends by many examples.

Mots clés: Controllability; Time optimal control; Lie groups; Linear systems

Domaines: Optimisation et contrôle [math.OC]

Philippe Jouan. Controllability of Linear Systems on Lie Groups. Journal of Dynamical and Control Systems, 2011, 17 (4), pp.591-616. ⟨hal-00541489⟩