Mixed H2/H∞ filtering by the theory of nash games
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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 , 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.
KeywordsControl Problem Nash Equilibrium Linear Estimator Nash Game State Estimation Error
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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
- D. J. N. Limebeer, B. D. O. Anderson and B. Hendel, “Nash games and mixed H 2/H ∞ control,” preprintGoogle Scholar
- D. J. N. Limebeer and U. Shaked, “Minimax terminal state estimation and H ∞ filtering,” submitted to IEEE Trans. Auto. ControlGoogle Scholar