Infinite time horizon nonzero-sum linear quadratic stochastic differential games with state and control-dependent noise

Abstract

This paper discusses the infinite time horizon nonzero-sum linear quadratic (LQ) differential games of stochastic systems governed by Ito’s equation with state and control-dependent noise. First, the nonzero-sum LQ differential games are formulated by applying the results of stochastic LQ problems. Second, under the assumption of mean-square stabilizability of stochastic systems, necessary and sufficient conditions for the existence of the Nash strategy are presented by means of four coupled stochastic algebraic Riccati equations. Moreover, in order to demonstrate the usefulness of the obtained results, the stochastic H-two/H-infinity control with state, control and external disturbance-dependent noise is discussed as an immediate application.