Invariant measures and controllability of finite systems on compact manifolds

Philippe Jouan

ESAIM: Control, Optimisation and Calculus of Variations (2012)

  • Volume: 18, Issue: 3, page 643-655
  • ISSN: 1292-8119

Abstract

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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, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.

How to cite

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Jouan, Philippe. "Invariant measures and controllability of finite systems on compact manifolds." ESAIM: Control, Optimisation and Calculus of Variations 18.3 (2012): 643-655. <http://eudml.org/doc/277822>.

@article{Jouan2012,
abstract = {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, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces. },
author = {Jouan, Philippe},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Compact homogeneous spaces; linear systems; controllability; finite dimensional Lie algebras; Haar measure; compact homogeneous spaces},
language = {eng},
month = {11},
number = {3},
pages = {643-655},
publisher = {EDP Sciences},
title = {Invariant measures and controllability of finite systems on compact manifolds},
url = {http://eudml.org/doc/277822},
volume = {18},
year = {2012},
}

TY - JOUR
AU - Jouan, Philippe
TI - Invariant measures and controllability of finite systems on compact manifolds
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2012/11//
PB - EDP Sciences
VL - 18
IS - 3
SP - 643
EP - 655
AB - 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, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.
LA - eng
KW - Compact homogeneous spaces; linear systems; controllability; finite dimensional Lie algebras; Haar measure; compact homogeneous spaces
UR - http://eudml.org/doc/277822
ER -

References

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  12. G.D. Mostow, Homogeneous spaces with finite invariant measure. Ann. Math.75 (1962) 17–37.  
  13. V.V. Nemytskii and V.V. Stepanov, Qualitative Theory of Differential Equations. Princeton Uniersity Press (1960).  
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  15. L. San Martin and V. Ayala, Controllability properties of a class of control systems on Lie groups, Nonlinear control in the year 20001, Paris, Lecture Notes in Control and Inform. Sci.258. Springer (2001) 83–92.  

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