Download PDF - Controllability of right invariant systems on semi-simple Lie groupsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Controllability of right invariant systems on semi-simple Lie groups

Authors 1, 2, 3

Affiliations

  1. INSA de Rouen, LMI, AMS, URA CNRS 1378, BP 08, Place Emile Blondel, 76131 Mont St Aignan, France
  2. INSA de Rouen, LMI, AMS, URA CNRS 1378, BP 08, Place Emile Blondel, 76131 Mont St Aignan, France, Institut Universitaire de France
  3. Department of Mathematics, University of Toronto, 100 St Georges Street, Toronto, Ontario, M5S-1A1, Canada

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.

Keywords

ENG
invariant vector fields, controllability, root systems, semi-simple Lie algebras

Bibliography

  1. [B] N. Bourbaki, Groupes et algèbres de Lie, Fasc. XXXVIII, chap. 7-8, Hermann, Paris, 1975.
  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.
  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 F4, G2, Bn and Cn, 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.
  6. [GB] J. P. Gauthier et G. Bornard, Controllabilité des systèmes bilinéaires, SIAM J. Control Optim. 20 (1982), 377-384.
  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.
  8. [H] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962.
  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.
  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.
  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.
  13. [L] J. D. Lawson, Maximal subsemigroups of Lie groups that are total, Proc. Edinburgh Math. Soc. 30 (1987), 479-501.
  14. [LC] F. S. Leite and P. E. Crouch, Controllability on classical Lie groups, Math. Control Signals Systems 1, 1988, 31-42.
  15. [W] G. Warner, Harmonic Analysis on Semi-simple Lie Groups 1, Springer, Berlin, 1972.
Banach Center Publications
1995/32/1
Export to PBN, Opens in new tab
Pages:
199-208
Main language of publication
English
Published
1995
Exact and natural sciences