Guaranteed cost control for uncertain stochastic systems with multiple decision makers via static output feedback

Abstract

This paper investigates the design of static output feedback controllers for a class of uncertain stochastic systems with multiple decision makers. The necessary conditions, which are determined from Karush-Kuhn-Tucker (KKT) conditions, for the existence of a guaranteed cost controller have been derived on the basis of the solutions of cross-coupled stochastic algebraic Riccati equations (CSAREs). It is shown that, if the solution of the CSAREs exists, the closed-loop system is exponentially mean square stable (EMSS) and its performance has an upper cost bound under uncertainties. In order to obtain the strategy set, Newton's method and a new sequential algorithm for solving the CSAREs are developed. Finally, a numerical example for a practical megawatt-frequency control problem shows that the proposed methods can help in attaining an adequate cost bound.