Non-Zero Sum Nash Game for Discrete-Time Infinite Markov Jump Stochastic Systems with Applications

Abstract

This paper is to study finite horizon linear quadratic (LQ) non-zero sum Nash game for discrete-time infinite Markov jump stochastic systems (IMJSSs). Based on the theory of stochastic analysis, a countably infinite set of coupled generalized algebraic Riccati equations are solved and a necessary and sufficient condition for the existence of Nash equilibrium points is obtained. From a new perspective, the finite horizon mixed robust H2/H∞ control is investigated, and summarize the relationship between Nash game and H2/H∞ control problem. Moreover, the feasibility and validity of the proposed method has been proved by applying it to a numerical example.

Keywords

• infinite Markov jump stochastic systems (IMJSSs)
• Nash equilibrium points
• coupled generalized algebraic Riccati equations
• Nash game
• <i>H</i>₂/<i>H</i>_∞ control