Set-Valued Estimation of State and Parameter Vectors within Adaptive Control Systems

  • V. M. Kuntsevich

Abstract

The problem under consideration is that of obtaining simultaneously set-valued estimates for state and parameter vectors of linear (in parameters and in phase coordinates) discrete-time systems under uncontrollable bounded disturbances and given bounded noise in measurements.

There is no other a priori information on disturbances and noise except for they are bounded. It is shown that in the absence of noise in measurements and in the presence only of uncontrollable additive disturbances having an effect on stationary plants being investigated, the problem of obtaining set-valued parameter estimates is equivalent to the problem of determining a set-valued solution of a set of linear algebraic equations under uncertainty in their right-hand sides. With additive measurement noise, set-valued estimation procedure should be changed considerably since in this case one has to determine the whole set of solutions of a set of algebraic equations under uncertainty in coefficients as well as in right-hand sides. The problem of simultaneous estimation of state and parameter vectors can be reduced in the long run to the last-mentioned algebraic one.

The problem of set-valued estimation for nonstationary systems with restricted parameter drift rate is also considered.

Keywords

Parameter Vector Linear Algebraic Equation Convex Polyhedron Posteriori Estimate Adaptive Control System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    F. C. Schweppe, Uncertain Dynamic Systems, Prentice-Hall, Englewood Cliffs, NJ (1973).Google Scholar
  2. 2.
    F. L. Chernousko and A. A. Melikjan, Game Problems of Control and Search, Nauka, Moscow, Russia (1973).Google Scholar
  3. 3.
    A. B. Kurzhanski, Control and Observation Under Conditions of Uncertainty, Nauka, Moscow, Russia (1977).Google Scholar
  4. 4.
    V. M. Kuntsevich and M. M. Lychak, Autom. Remote Control 1, 77 (1979).Google Scholar
  5. 5.
    G. M. Bakan, Sov. Autom. Control 2, 38 (1980).Google Scholar
  6. 6.
    M. Milanese and G. Belforte, IEEE Trans. Autom. Control AC-27, 408 (1982).MathSciNetCrossRefGoogle Scholar
  7. 7.
    G. M. Bakan, Autom. Remote Control 9, 81 (1980).Google Scholar
  8. 8.
    V. M. Kuntsevich and M. M. Lychak, Synthesis of Optimal and Adaptive Control Systems: Game Approach, Naukova dumka, Kiev, Russia (1985).MATHGoogle Scholar
  9. 9.
    J. P. Norton, Inter. J. Control 45 375 (1987).MATHCrossRefGoogle Scholar
  10. 10.
    F. L. Chernousko, Estimation of the Phase State of Dynamic Systems, Nauka, Moscow, Russia (1988).Google Scholar
  11. 11.
    V. M. Kuntsevich, M. M. Lychak and A. S. Nikitenko, in: 8th IFAC/IFORS Symposium, Vol. 2, pp. 1237-1241, Beijing, P.R. China (1988).Google Scholar
  12. 12.
    A. B. Kurzhanski, Identification Theory of Guaranteed Estimates, IIASA Working Paper, Laxenburg, Austria (1989).Google Scholar
  13. 13.
    H. Piet-Lahanier and E. Walter, in: Proceedings of the 28th IEEE Conference on Decision and Control Tampa, FL (1989).Google Scholar
  14. 14.
    M. Milanese and A. Vicino, Automatica 27, 403 (1991).MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    G. M. Bakan and N. N. Kussul, Avtomatika 5, 11 (1989).MathSciNetGoogle Scholar
  16. 16.
    E. Walter and H. Piet-Lahanier, Math. Comp. Sim. 32, 468 (1990).Google Scholar
  17. 17.
    G. M. Bakan and N. N. Kussul, Avtomatika 3, 29 (1990).MathSciNetGoogle Scholar
  18. 18.
    D. C. N. Tse, M. A. Dahleh and I. N. Tsitsikeis, in: Proceedings of the 1991 IEEE Conference on Decision and Control, pp. 623-628, Brighton, United Kingdom (1991).Google Scholar
  19. 19.
    S. M. Veres and J. P. Norton, Inter. J. Control 50, 639 (1989).MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    A. B. Kurzhanski and I. Valyi, in: Nonlinear Synthesis, Progress in Systems and Control Theory (Ch. I. Byrnes and A. B. Kurzhanski, eds.) Birkhauser, Boston, MA, pp. 184–196 (1991).Google Scholar
  21. 21.
    A. B. Kurzhanski, Avtom. Telemekh. 4, 3 (1991).Google Scholar
  22. 22.
    M. Milanese and A. Vicino, Automatica 27, 977 (1991).Google Scholar
  23. 23.
    V. M. Kuntsevich and M. M. Lychak, in: Lecture Notes in Control and Information Sciences, 196, Springer-Verlag, Berlin, Germany (1992).Google Scholar
  24. 24.
    V. M. Kuntsevich, M. M. Lychak, and A. S. Niktienko, Kibernetika 4, 47 (1988).Google Scholar
  25. 25.
    V. M. Kuntsevich, Dokl. AN SSR 288, 321 (1986).MathSciNetGoogle Scholar
  26. 26.
    R. E. Kaiman, Us. Mat. Nauk 10, 117 (1984).Google Scholar
  27. 27.
    R. E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliffs, NJ (1966).MATHGoogle Scholar
  28. 28.
    R. E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliffs, NJ (1966).MATHGoogle Scholar
  29. 29.
    V. M. Kuntsevich, Avtom. Telemekh. 2, 79 (1980).MathSciNetGoogle Scholar
  30. 30.
    V. M. Kuntsevich and A. S. Nikitenko, Kibernetika 5, 38 (1990).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • V. M. Kuntsevich
    • 1
  1. 1.Academy of Sciences of UkraineV. M. Glushkov Institute of CyberneticsKievUkraine

Personalised recommendations