Method of Moment Restrictions in Robust Control and Filtering

Abstract

The minimax control and filtering problems are considered for the linear MIMO system acted on by a stochastic input. The input has a meaning of the disturbance in the control problem and it consists of the noise and signal in the filtering one. The performance index is the maximum of the system output variance over the class of inputs, which is specified by the moment restrictions. The problem is to minimize the performance index over the given class of regulators or filters. It includes the H2 and H∞ optimal control and filtering problems as the special cases. The solution obtained involves the solution of some auxiliary convex optimization problem and the solution of the standard model-matching problem. The approach is based on the theory of generalized Chebyshev-type inequalities.