Stochastic Nash Games for Markov Jump Linear Systems with State- and Control-Dependent Noise

Abstract

This paper investigates Nash games for a class of linear stochastic systems governed by Ito’s differential equation with Markovian jump parameters both in finite-time horizon and infinite-time horizon. First, stochastic Nash games are formulated by applying the results of indefinite stochastic linear quadratic (LQ) control problems. Second, in order to obtain Nash equilibrium strategies, cross-coupled stochastic Riccati differential (algebraic) equations (CSRDEs and CSRAEs) are derived. Moreover, in order to demonstrate the validity of the obtained results, stochastic H 2/H ∞ control with state- and control-dependent noise is discussed as an immediate application. Finally, a numerical example is provided.