A numerical computation of linear quadratic dynamic games for stochastic systems with state- and control-dependent noise

In this paper, we discuss infinite-horizon linear quadratic Pareto-optimal control problems and Nash games, respectively, for stochastic systems with state- and control-dependent noise. The analytical and computational approaches for solving the cross-coupled algebraic Riccati equations (CSAREs) which are related with Pareto strategies and Nash strategies are developed. The new iterative algorithms based on the Linear Matrix Inequality (LMI) are proposed to design the strategy set. The efficiency of the proposed algorithms are demonstrated by solving a numerical example of a third-order synchronous machine and a first-order exciter regulator system.