Linear discrete-time H_∞-optimal tracking with preview

The problem of finite-time H_∞-tracking for linear, discrete, time-varying systems is considered. No a priori knowledge of the dynamics of the reference signal is assumed. A distinction between three cases is made, depending on whether the reference signal is perfectly known in advance, measured on-line, or previewed in a fixed interval of time ahead. The tracking problem is formulated as a game, where the controller plays against nature which may choose the initial condition of the system and any energy bounded driving disturbance and measurement noise inputs. Necessary and sufficient conditions are derived for the existence of saddle-point equilibrium solutions to the three different information structures of the reference, and the corresponding tracking controllers are derived.