Robust discrete-time H_∞-optimal tracking with preview

The problem of robust, finite-time, H_∞-tracking for linear, discrete, time-varying systems is considered from the game theory point of view. No a priori knowledge of the dynamic model of the reference signal to be tracked is assumed, and the parameters of the system are not completely known. Two tracking problems are investigated, depending on whether the reference signal is perfectly known in advance, or previewed in a fixed-interval of time ahead. An augmented state-space description that converts the parameter uncertainty to bounded energy signal is used. A tracking game is then defined and solved. It is shown that its saddle-point equilibrium, if it exists, guarantees a prescribed H_∞-norm performance of the tracker, for all possible parameters.