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)


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.


Control Problem Nash Equilibrium Linear Estimator Nash Game State Estimation Error 
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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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