Controllability of right invariant systems on semi-simple Lie groups

R. El Assoudi; J. Gauthier; I. Kupka

Banach Center Publications (1995)

  • Volume: 32, Issue: 1, page 199-208
  • ISSN: 0137-6934

Abstract

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We deal with controllability of right invariant control systems on semi-simple Lie groups. We recall the history of the problem and the successive results. We state the final complete result, with a sketch of proof.

How to cite

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El Assoudi, R., Gauthier, J., and Kupka, I.. "Controllability of right invariant systems on semi-simple Lie groups." Banach Center Publications 32.1 (1995): 199-208. <http://eudml.org/doc/262629>.

@article{ElAssoudi1995,
abstract = {We deal with controllability of right invariant control systems on semi-simple Lie groups. We recall the history of the problem and the successive results. We state the final complete result, with a sketch of proof.},
author = {El Assoudi, R., Gauthier, J., Kupka, I.},
journal = {Banach Center Publications},
keywords = {invariant vector fields; controllability; root systems; semi-simple Lie algebras; Lie saturate; rank condition; right invariant; Lie group},
language = {eng},
number = {1},
pages = {199-208},
title = {Controllability of right invariant systems on semi-simple Lie groups},
url = {http://eudml.org/doc/262629},
volume = {32},
year = {1995},
}

TY - JOUR
AU - El Assoudi, R.
AU - Gauthier, J.
AU - Kupka, I.
TI - Controllability of right invariant systems on semi-simple Lie groups
JO - Banach Center Publications
PY - 1995
VL - 32
IS - 1
SP - 199
EP - 208
AB - We deal with controllability of right invariant control systems on semi-simple Lie groups. We recall the history of the problem and the successive results. We state the final complete result, with a sketch of proof.
LA - eng
KW - invariant vector fields; controllability; root systems; semi-simple Lie algebras; Lie saturate; rank condition; right invariant; Lie group
UR - http://eudml.org/doc/262629
ER -

References

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  1. [B] N. Bourbaki, Groupes et algèbres de Lie, Fasc. XXXVIII, chap. 7-8, Hermann, Paris, 1975. Zbl0329.17002
  2. [BJKS] B. Bonnard, V. Jurdjevic, I. Kupka and G. Sallet, Transitivity of families of invariant vector fields on the semi-direct products of Lie groups, Trans. Amer. Math. Soc. 271 (1982), 525-535. Zbl0519.49023
  3. [EA] R. El Assoudi, Accessibilité par des champs de vecteurs invariants à droite sur un groupe de Lie, Thèse de doctorat de l'Université Joseph Fourier, Grenoble, 1991. 
  4. [EAG] R. El Assoudi and J. P. Gauthier, Controllability of right invariant systems on real simple Lie groups of type F 4 , G 2 , B n and C n , Math. Control Signals Systems 1 (1988), 293-301. 
  5. [EAGK] R. El Assoudi, J. P. Gauthier and I. Kupka, Controllability of right invariant systems on semi-simple Lie groups, Ann. Inst. Henri Poincaré, to appear. Zbl0839.93019
  6. [GB] J. P. Gauthier et G. Bornard, Controllabilité des systèmes bilinéaires, SIAM J. Control Optim. 20 (1982), 377-384. Zbl0579.93005
  7. [GKS] J. P. Gauthier, I. Kupka and G. Sallet, Controllability of right invariant systems on real simple Lie groups, Systems Control Letters 5 (1984), 187-190. Zbl0552.93010
  8. [H] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962. Zbl0111.18101
  9. [HHL] J. Hilgert, K. Hoffman and J. D. Lawson, Controllability of systems on a nilpotent Lie group, Beitr. Algebra Geom. 30 (1985), 185-190. 
  10. [HI] J. Hilgert, Max. semigroups and controllability in products of Lie groups, Arch. Math. (Basel) 49 (1987), 189-195. Zbl0649.22003
  11. [J] A. Joseph, The minimal orbit in a simple Lie algebra and its associated maximal ideal, Ann. Sci. Ecole Norm. Sup. (4) 9 (1976), 1-29. Zbl0346.17008
  12. [JK] V. Jurdjevic and I. Kupka, Controllability of right invariant systems on semi-simple Lie groups and their homogeneous spaces, Ann. Inst. Fourier (Grenoble) 31 (4) (1981), 151-179. Zbl0453.93011
  13. [L] J. D. Lawson, Maximal subsemigroups of Lie groups that are total, Proc. Edinburgh Math. Soc. 30 (1987), 479-501. Zbl0649.22004
  14. [LC] F. S. Leite and P. E. Crouch, Controllability on classical Lie groups, Math. Control Signals Systems 1, 1988, 31-42. Zbl0658.93013
  15. [W] G. Warner, Harmonic Analysis on Semi-simple Lie Groups 1, Springer, Berlin, 1972. Zbl0265.22020

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