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Invariant measures and controllability of finite systems on compact manifolds

Philippe Jouan — 2012

ESAIM: Control, Optimisation and Calculus of Variations

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 [Ph. Jouan, 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.

Invariant measures and controllability of finite systems on compact manifolds

Philippe Jouan — 2012

ESAIM: Control, Optimisation and Calculus of Variations

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 [Ph. Jouan, (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.

Invariant measures and controllability of finite systems on compact manifolds

Philippe Jouan — 2012

ESAIM: Control, Optimisation and Calculus of Variations

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 [Ph. Jouan, (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.

Equivalence of control systems with linear systems on Lie groups and homogeneous spaces

Philippe Jouan — 2010

ESAIM: Control, Optimisation and Calculus of Variations

The aim of this paper is to prove that a control affine system on a manifold is equivalent by diffeomorphism to a linear system on a Lie group or a homogeneous space if and only if the vector fields of the system are complete and generate a finite dimensional Lie algebra. A vector field on a connected Lie group is linear if its flow is a one parameter group of automorphisms. An affine vector field is obtained by adding a left invariant one. Its projection on a homogeneous space, whenever...

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