Nash strategy of multiparameter singularly perturbed Markov jump stochastic systems with state- and control-dependent noise

Abstract

This paper investigates Nash games for a class of multiparameter singularly perturbed stochastic systems governed by Ito's differential equation with Markov jump parameters with state- and control-dependent noise. First, in order to obtain Nash equilibrium strategies, cross-coupled stochastic algebraic Riccati equations (CSAREs) are introduced. After establishing an asymptotic structure with positive definiteness for solutions of CSAREs, feasible numerical algorithms by means of the linear matrix inequality (LMI) are considered. In addition, the mode-independent Nash strategy set is also investigated. Finally, we provide a numerical example to verify the efficiency of the proposed algorithms.