Design of minimax controllers for linear systems with non‐zero initial states under specified information structures

In this paper, we obtain the solution to the discrete‐time, linear‐quadratic, finite‐horizon disturbance rejection problem, with hard bounds on the disturbance and with a known or an unknown non‐zero initial state. It is shown that there exist two regions 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 paper also develops a general algorithm for the construction of such saddle points under different information structures, and illustrates this algorithm on a numerical example.