Forward invariant sets, homogeneity and small-time local controllability

Mikhail Krastanov

Banach Center Publications (1995)

  • Volume: 32, Issue: 1, page 287-300
  • ISSN: 0137-6934

Abstract

top
The property of forward invariance of a subset of R n 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.

How to cite

top

Krastanov, Mikhail. "Forward invariant sets, homogeneity and small-time local controllability." Banach Center Publications 32.1 (1995): 287-300. <http://eudml.org/doc/262846>.

@article{Krastanov1995,
abstract = {The property of forward invariance of a subset of $R^n$ 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.},
author = {Krastanov, Mikhail},
journal = {Banach Center Publications},
keywords = {small-time local controllability; forward invariant sets; differential inclusions; homogeneous control systems; forward invariant},
language = {eng},
number = {1},
pages = {287-300},
title = {Forward invariant sets, homogeneity and small-time local controllability},
url = {http://eudml.org/doc/262846},
volume = {32},
year = {1995},
}

TY - JOUR
AU - Krastanov, Mikhail
TI - Forward invariant sets, homogeneity and small-time local controllability
JO - Banach Center Publications
PY - 1995
VL - 32
IS - 1
SP - 287
EP - 300
AB - The property of forward invariance of a subset of $R^n$ 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.
LA - eng
KW - small-time local controllability; forward invariant sets; differential inclusions; homogeneous control systems; forward invariant
UR - http://eudml.org/doc/262846
ER -

References

top
  1. [1] P. Brunovský, Local controllability of odd systems, in: Banach Center Publ. 1, PWN, Warszawa, 1976, 39-45. Zbl0344.93016
  2. [2] R. Bianchini and G. Stefani, Sufficient conditions on local controllability, in: Proc. 25th IEEE Conf. Decision & Control, Athens, 1986, 967-970. 
  3. [3] R. Bianchini and G. Stefani, Graded approximations and controllability along a trajectory, SIAM J. Control Optim. 28 (1990), 903-924. Zbl0712.93005
  4. [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. Zbl0417.49048
  5. [5] F. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1983. Zbl0582.49001
  6. [6] H. Hermes, Control systems with generate decomposable Lie algebras, J. Differential Equations 44 (1982), 166-187. Zbl0496.49021
  7. [7] H. Hermes, Nilpotent and high-order approximations of vector field systems, SIAM Rev. 33 (1991), 238-264. Zbl0733.93062
  8. [8] M. Kawski, A necessary condition for local controllability, Contemp. Math. 68 (1987), 143-155. 
  9. [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. [10] M. Krastanov, A necessary condition for local controllability, C. R. Acad. Bulgare Sci. 41 (7) (1988), 13-15. Zbl0850.93098
  11. [11] C. Lobry, Sur l'ensemble des points atteignables par les solutions d'une équation différentielle multivoque, Publ. Math. Bordeaux 1 (5) (1973). 
  12. [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. [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. [14] H. Sussmann, Small-time local controllability and continuity of the optimal time function for linear systems, J. Optim. Theory Appl. (1988), 281-297. Zbl0596.93012
  15. [15] H. Sussmann, Lie brackets and local controllability: a sufficient condition for scalar-input systems, SIAM J. Control Optim. 21 (1983), 686-713. Zbl0523.49026
  16. [16] H. Sussmann, A general theorem on local controllability, ibid. 25 (1987), 158-194. Zbl0629.93012
  17. [17] V. Veliov, On the controllability of control constrained linear systems, Math. Balkanica 2 (2-3) (1988), 147-155. Zbl0681.93009
  18. [18] V. Veliov, On the Lipschitz continuity of the value function in optimal control, to appear. Zbl0901.49022
  19. [19] V. Veliov and M. Krastanov, Controllability of piecewise linear systems, Systems Control Lett. 7 (1986), 335-341. Zbl0609.93006

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.