A game theoretic approach to the optimal control of uncertain systems

Abstract

The issue of performance robustness is considered in a dynamic games framework where the god is to find a feedback controller that stabilizes the system under all plant perturbations and that minimizes the value of a quadratic performance index under the worst perturbations. To find a solution to this hard-constrained problem, an auxiliary soft-constrained dynamic game problem is formulated. It is shown that the solution to the auxiliary problem provides the solution to the original problem, under the assumption that the solution to the original problem occurs on the boundary of the perturbations set. The approach, however, can still be applied, with modifications, to the case when this assumption fails. Copyright (C) 1996 Elsevier Science Ltd.