Abstract
AbstractIn this paper, we consider infinite horizon linear‐quadratic (LQ) Nash games for stochastic differential equations (SDEs) with infinite Markovian jumps and (x,u,v)‐dependent noise. An indefinite stochastic LQ result is first derived for the considered system. Then, under the condition of strong detectability, a necessary and sufficient condition for the existence of a Nash equilibrium is put forward in terms of the solvability of a countably infinite set of coupled generalized algebraic Riccati equations (ICGAREs). Moreover, the mixed H2/H∞ control is investigated by Nash game approach as an important application. At last, we present an iterative algorithm to solve the ICGAREs, and a numerical simulation is given to illustrate its efficiency.
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