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.
Keywords: compact homogeneous spaces, linear systems, controllability, finite dimensional Lie algebras, Haar measure
@article{COCV_2012__18_3_643_0,
author = {Jouan, Philippe},
title = {Invariant measures and controllability of finite systems on compact manifolds},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {643--655},
year = {2012},
publisher = {EDP Sciences},
volume = {18},
number = {3},
doi = {10.1051/cocv/2011165},
mrnumber = {3041659},
zbl = {1281.93020},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2011165/}
}
TY - JOUR AU - Jouan, Philippe TI - Invariant measures and controllability of finite systems on compact manifolds JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 643 EP - 655 VL - 18 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2011165/ DO - 10.1051/cocv/2011165 LA - en ID - COCV_2012__18_3_643_0 ER -
%0 Journal Article %A Jouan, Philippe %T Invariant measures and controllability of finite systems on compact manifolds %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 643-655 %V 18 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2011165/ %R 10.1051/cocv/2011165 %G en %F COCV_2012__18_3_643_0
Jouan, Philippe. Invariant measures and controllability of finite systems on compact manifolds. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 3, pp. 643-655. doi: 10.1051/cocv/2011165
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