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.
Mots-clés : 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},
publisher = {EDP-Sciences},
volume = {18},
number = {3},
year = {2012},
doi = {10.1051/cocv/2011165},
mrnumber = {3041659},
zbl = {1281.93020},
language = {en},
url = {http://archive.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 - http://archive.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 http://archive.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. http://archive.numdam.org/articles/10.1051/cocv/2011165/
[1] and , Basic Lie Theory. World Scientific (1997). | Zbl
[2] and , Géométrie différentielle : variétés, courbes et surfaces. Presses universitaires de France (1987). | MR | Zbl
[3] , Compact Clifford-Klein forms of symmetric spaces. Topology 2 (1963) 111-122. | MR | Zbl
[4] and , Local controllability for linear control systems on Lie groups. J. Dyn. Control Syst. 11 (2005) 353-373. | MR | Zbl
[5] , Structure des systèmes non linéaires. Éditions du CNRS, Paris (1984). | MR | Zbl
[6] , Differential Geometry and Symmetric Spaces. Academic Press (1962). | MR | Zbl
[7] , Equivalence of control systems with linear systems on Lie groups and homogeneous spaces. ESAIM : COCV 16 (2010) 956-973. | Numdam | MR | Zbl
[8] , Finite time and exact time controllability on compact manifolds. J. Math. Sci. (to appear). | MR | Zbl
[9] , Geometric control theory. Cambridge University Press (1997). | MR | Zbl
[10] and , Control systems on Lie groups. J. Differ. Equ. 12 (1972) 313-329. | MR | Zbl
[11] , Controllability of nonlinear systems on compact manifolds. SIAM J. Control. 12 (1974) 1-4. | MR | Zbl
[12] , Homogeneous spaces with finite invariant measure. Ann. Math. 75 (1962) 17-37. | MR | Zbl
[13] and , Qualitative Theory of Differential Equations. Princeton Uniersity Press (1960). | MR | Zbl
[14] , Controllability of invariant systems on Lie groups and homogeneous spaces. J. Math. Sci. 100 (2000) 2355-2427. | MR | Zbl
[15] and , Controllability properties of a class of control systems on Lie groups, Nonlinear control in the year 2000 1, Paris, Lecture Notes in Control and Inform. Sci. 258. Springer (2001) 83-92. | MR | Zbl
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