Nash Strategies of Markov Jump Stochastic Systems Applied to Weakly-Coupled Large-Scale Systems

Abstract

AbstractThis paper investigates Nash games for a class of linear stochastic systems governed by Itô's differential equation with Markov jump parameters. First, in order to obtain Nash equilibrium strategies, cross-coupled stochastic algebraic Riccati equations (CSAREs) are formulated. Moreover, necessary condition for the existence of solution for CSAREs is also developed. It is noteworthy that this is the first time that conditions for the existence of stochastic equilibria have been derived based on the solutions of sets of CSAREs. As another important application, large-scale weakly-coupled systems are investigated. After establishing an asymptotic structure with positive definiteness for CSAREs solutions, a feasible algorithm that is based on the linear matrix inequality (LMI) for solving CSAREs is considered. Finally, we provide a numerical example to verify the efficiency of the proposed algorithms.