Minimax control under a restriction on the moments of disturbance

Abstract

The discrete-time linear MIMO plant is considered, which is acted on by a stochastic disturbance. It is assumed that the disturbance is not known but belongs to the given class, which is specified by a restriction on the moments of disturbances. The cost function is the maximum of the closed-loop system controlled output variance over the class of disturbances. The problem is to construct the optimal linear stabilizing regulator. For the SISO plant the approach includes both H/sup 2/ and H/sup /spl infin// optimal controls as the special cases. The solution of the minimax control problem is obtained. The method proposed involves the solution of some auxiliary convex optimization problem and the solution of the model-matching problem. The criterion is obtained also to determine the worst case disturbance. The solution is based on the generalization of the Chebyshev-type inequalities.