Advertisement

Automation and Remote Control

, Volume 62, Issue 4, pp 590–596 | Cite as

Ellipsoidal State Estimates of Linear Dynamic Systems: Their Limiting Behavior

  • S. A. Nazin
Article

Abstract

In guaranteed estimation of the states of dynamic systems under deterministic bounded disturbances, use of made of outer ellipsoidal estimates that are optimal relative to the volume and sum of squares of the semiaxes of the ellipsoid. The boundedness and convergence of a sequence of such ellipsoids for stable discrete systems are investigated. The asymptotic behavior of these estimates mostly depends on the minimality criterion chosen for the ellipsoid dimension.

Keywords

Dynamic System Mechanical Engineer Asymptotic Behavior System Theory State Estimate 
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.
    Schweppe, F., Uncertain Dynamic Systems, New York: Prentice Hall, 1973.Google Scholar
  2. 2.
    Chernoys'ko, F.L., Otsenivanie fazovogo sostoyaniya dinamicheskikh sistem (Estimation of the Phase State of Dynamic Systems), Moscow: Nauka, 1988.Google Scholar
  3. 3.
    Fogel, E. and Huang, Y., On the Value of Information in System Identification-Bounded Noise Case, Automatica, 1982, pp. 229–238.Google Scholar
  4. 4.
    Kiselev, O.N. and Polyak, B.T., Ellipsoidal Estimation by the Generalized Criterion, Avtom. Telemekh., 1991, no. 9, pp. 133–144.Google Scholar
  5. 5.
    Ovseevich, A.I. and Reshetnyak, Yu.N., Asymptotic Behavior of Ellipsoidal Estimates of Reachability Domains. I, Tekh. Kibern., 1992, no. 1, pp. 90–100.Google Scholar
  6. 6.
    Ovseevich, A.I., Local Asymptotic Behavior of Bounding Ellipsoids of Reachability Domains, Avtom. Telemekh., 1994, no. 12, pp. 48–58.Google Scholar
  7. 7.
    Horn, R. and Jhonson, C., Matrix Analysis, New York: Cambridge Univ. Press, 1985. Translated under the title Matrichnyi analiz, Moscow: Mir, 1989.Google Scholar
  8. 8.
    Reshetnyak, Yu.N., Summation of Ellipsoids in Guaranteed Estimation, Prikl. Mat. Mekh., 1989, vol. 53, issue 2, pp. 259–264.Google Scholar

Copyright information

© MAIK “Nauka/Interperiodica” 2001

Authors and Affiliations

  • S. A. Nazin
    • 1
  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia

Personalised recommendations