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 Itô'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, crosscoupled 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.

Pareto Optimal Control for Uncertain Markov Jump Linear Stochastic Systems

“…By applying the well-known guaranteed cost control principle [7], the conditions, wherein the stochastic system is exponentially meansquare stable (EMSS) and has a cost bound, are given by the stochastic algebraic Riccati inequality (SARI). In contrast to the existing control strategy [3,4,5,6], it is more difficult for dynamic games to attain their equilibrium due to the complexity of the calculation of their cost bound. Hence, this research is a non-trivial extension of the existing results.…”

“…2 / ∞ control problem for a class of Markov jump linear stochastic systems with ( , , )-dependent noise involving multiple decision makers has been addressed [4]. Nash games and the related 2 / ∞ control for a class of linear stochastic systems with Markovian jump parameters, both in finite-time and infinite-time horizon, have been studied [5]. In [6], the stochastic non-cooperative differential game theory of generalized linear Markov jump systems and its applications have been studied extensively.…”