On minimaxity criteria of a linear regulator for known and uncertain systems

Abstract

A complete solution in both time and frequency domains is given for the following inverse minimax control problem: under what conditions a given state feedback of a linear continuous-time system is a minimax control with respect to some quadratic performance index with a non-negative state weighting, under the assumption that the positive weight on the control and the negative weight on the the disturbance are fixed. When the weight on the disturbance approaches co, the frequency criterion of minimaxity obtained here reduces to the well-known criterion of optimality for an unforced system proposed by Kalman. Further, a local approach is used to solve the inverse problem of the minimax robust control for uncertain systems, in which the uncertainties are supposed to be either norm bounded or linear combination. It is shown how these results are applied to solving the inverse problem of H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> , suboptimal control.