GENERAL APPROACH TO THE ESTIMATION AND CONTROL OF LINEAR SYSTEMS WITH UNCERTAIN STATISTICS.

The problem of minimax design of linear observers and regulators for linear time-varying multivariable stochastic systems with uncertain models of their second-order statistics is treated. Completely general classes of allowable covariance matrices and means of the process and observation noises and of the random initial condition are considered. A game formulation of the problem is adopted and minimax theorems are shown to hold for each of the filtering situations analyzed. Conditions satisfied by the saddlepoint solutions are derived.