Download PDF - Controllability of nilpotent systemsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Controllability of nilpotent systems

Authors 1

Affiliations

  1. Departamento de Matemática, Universidad Católica del Norte Casilla, 1280, Antofagasta, Chile

Abstract

In this paper we study the controllability property of invariant control systems on Lie groups. In [1], the authors state: ``If there exists a real function strictly increasing on the positive trajectories, then the system cannot be controllable". To develop this idea, the authors define the concept of symplectic vector via the co-adjoint representation. We are interested in finding algebraic conditions to determine the existence of symplectic vectors in nilpotent Lie algebras. In particular, we state a necessary and sufficient condition for controllability in the simply connected nilpotent case.

Bibliography

  1. V. Ayala and L. Vergara, Co-adjoint representation and controllability, Proyecciones 11 (1992), 37-48.
  2. B. Bonnard, V. Jurdjevic, I. Kupka and G. Sallet, Transitivity of invariant vector fields on the semidirect product of Lie groups, Trans. Amer. Math. Soc. 271 (1982), 521-535.
  3. R. Brockett, Systems theory on group manifolds and coset spaces, SIAM J. Control 10 (1972), 265-284.
  4. L. Corwin and F. Greenleaf, Representations of Nilpotent Lie Groups and Their Applications, Part I, Cambridge University Press, 1990.
  5. V. Jurdjevic and I. Kupka, Control systems on semi-simple Lie groups and their homogeneous spaces, Ann. Inst. Fourier (Grenoble) 31 (4) (1981), 151-179.
  6. V. Jurdjevic and H. Sussmann, Control systems on Lie groups, J. Differential Equations 12 (1972), 313-329.
  7. I. Kupka, Introduction to the Theory of Systems, 16 Coloquio Brasileiro de Matematica, 1987.
  8. L. San Martin and P. Crouch, Controllability on principal fibre bundle with compact structure group, Systems Control Letters 5 (1984), 35-40.
  9. H. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180 (1973), 171-188.
Banach Center Publications
1995/32/1
Export to PBN, Opens in new tab
Pages:
35-46
Main language of publication
English
Published
1995
Exact and natural sciences