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Mixed H2/H filtering by the theory of nash games

  • D. J. N. Limebeer
  • B. D. O. Anderson
  • B. Hendel
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 183)

Abstract

The aim of this paper is to study an H 2/H terminal state estimation problem using the classical theory of Nash equilibria. The H 2/H nature of the problem comes from the fact that we seek an estimator which satisfies two Nash inequalities. The first reflects an H filtering requirement in the sense alluded to in [4], while the second inequality demands that the estimator be optimal in the sense of minimising the variance of the terminal state estimation error. The problem solution exploits a duality with the H 2/H control problem studied in [2, 3]. By exploiting duality in this way, one may quickly extablish that an estimator exists which staisfies the two Nash inequalities if and only if a certain pair of cross coupled Riccati equations has a solution on some optimisation interval. We conclude the paper by showing that the Kalman filtering, H filtering and H 2/H filtering problems may all be captured within a unifying Nash game theoretic framework.

Keywords

Control Problem Nash Equilibrium Linear Estimator Nash Game State Estimation Error 
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.

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References

  1. [1]
    T. Basar and G. J. Olsder, “Dynamic noncooperative game theory,” Academic Press, New York, 1982zbMATHGoogle Scholar
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    D. J. N. Limebeer, B. D. O. Anderson and B. Hendel, “A Nash game approach to mixed H 2/H control,” submitted for publicationGoogle Scholar
  3. [3]
    D. J. N. Limebeer, B. D. O. Anderson and B. Hendel, “Nash games and mixed H 2/H control,” preprintGoogle Scholar
  4. [4]
    D. J. N. Limebeer and U. Shaked, “Minimax terminal state estimation and H filtering,” submitted to IEEE Trans. Auto. ControlGoogle Scholar
  5. [5]
    A. W. Starr and Y. C. Ho, “Nonzero-sum differential games,” J. Optimization Theory and Applications, Vol. 3, No. 3, pp 184–206, 1967CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • D. J. N. Limebeer
    • 1
  • B. D. O. Anderson
    • 2
  • B. Hendel
    • 1
  1. 1.Department of Electrical EngineeringImperial CollegeLondon
  2. 2.Department of Systems EngineeringAustralian National UniversityCanberraAustralia

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