Design of minimax controllers for linear systems with nonzero initial conditions and under specified information structures

The solution is obtained to the discrete-time, linear-quadratic, finite-horizon disturbance rejection problem, with hard bounds on the disturbance. It is shown that two regions can be identified in the space of initial conditions: one where a pure-strategy saddle point exists, and the other where no pure-strategy saddle point exists. In the latter region, the structure of the minimax controller is fixed throughout, and a saddle point exists in the class of mixed policies. The construction of such saddle points is discussed. Minimax controllers are obtained for the case in which no information is available to the controller, i.e., the open-loop case. Subsequently, these results are used in solving for minimax controllers with more general information structures.