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ArticleOriginal scientific text

Title

Forward invariant sets, homogeneity and small-time local controllability

Authors 1

Affiliations

  1. Department of Operations Research, Institute of Mathematics, Bl. Acad. G. Bonchev 8, 1113 Sofia, Bulgaria

Abstract

The property of forward invariance of a subset of Rn with respect to a differential inclusion is characterized by using the notion of a perpendicular to a set. The obtained results are applied for investigating the dependence of the small-time local controllability of a homogeneous control system on parameters.

Keywords

ENG
small-time local controllability, forward invariant sets, differential inclusions, homogeneous control systems

Bibliography

  1. P. Brunovský, Local controllability of odd systems, in: Banach Center Publ. 1, PWN, Warszawa, 1976, 39-45.
  2. R. Bianchini and G. Stefani, Sufficient conditions on local controllability, in: Proc. 25th IEEE Conf. Decision & Control, Athens, 1986, 967-970.
  3. R. Bianchini and G. Stefani, Graded approximations and controllability along a trajectory, SIAM J. Control Optim. 28 (1990), 903-924.
  4. R. Bianchini and G. Stefani, Self-accessibility of a set with respect to a multivalued field, J. Optim. Theory Appl. 31 (1980), 535-552.
  5. F. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1983.
  6. H. Hermes, Control systems with generate decomposable Lie algebras, J. Differential Equations 44 (1982), 166-187.
  7. H. Hermes, Nilpotent and high-order approximations of vector field systems, SIAM Rev. 33 (1991), 238-264.
  8. M. Kawski, A necessary condition for local controllability, Contemp. Math. 68 (1987), 143-155.
  9. M. Kawski, High-order small time local controllability, in: Nonlinear Controllability and Optimal Control, H. Sussmann (ed.), Marcel Dekker, New York, 1990, 431-467.
  10. M. Krastanov, A necessary condition for local controllability, C. R. Acad. Bulgare Sci. 41 (7) (1988), 13-15.
  11. C. Lobry, Sur l'ensemble des points atteignables par les solutions d'une équation différentielle multivoque, Publ. Math. Bordeaux 1 (5) (1973).
  12. G. Stefani, On the local controllability of a scalar input control system, in: Theory and Applications of Nonlinear Control Systems, C. Byrnes and A. Lindquist (eds.), Elsevier Science Publ., 1986, 167-179.
  13. G. Stefani, Polynomial approximation to control systems and local controllability, in: Proc. 25th IEEE Conf. on Decision & Control, Ft. Landerdale, 1985, 33-38.
  14. H. Sussmann, Small-time local controllability and continuity of the optimal time function for linear systems, J. Optim. Theory Appl. (1988), 281-297.
  15. H. Sussmann, Lie brackets and local controllability: a sufficient condition for scalar-input systems, SIAM J. Control Optim. 21 (1983), 686-713.
  16. H. Sussmann, A general theorem on local controllability, ibid. 25 (1987), 158-194.
  17. V. Veliov, On the controllability of control constrained linear systems, Math. Balkanica 2 (2-3) (1988), 147-155.
  18. V. Veliov, On the Lipschitz continuity of the value function in optimal control, to appear.
  19. V. Veliov and M. Krastanov, Controllability of piecewise linear systems, Systems Control Lett. 7 (1986), 335-341.
Banach Center Publications
1995/32/1
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Pages:
287-300
Main language of publication
English
Published
1995
Exact and natural sciences