MIXED H2/H-INFINITY FILTERING BY THE THEORY OF NASH GAMES

The aim of this paper is to study an H-2/H(infinity) terminal state estimation problem using the classical theory of Nash equilibria. The H-2/H(infinity) nature of the problem comes from the fact that we seek an estimator which satisfies two Nash inequalities. The first reflects an H(infinity) 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(infinity) 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(infinity) filtering and H-2/H(infinity) filtering problems may all be captured within a unifying Nash game theoretic framework.