Static output feedback strategy of stochastic Nash games for weakly-coupled large-scale systems

This paper discusses the infinite horizon static output feedback Nash games for stochastic weakly-coupled large-scale systems with state-dependent noise. It is shown that the conditions for the existence of Nash equilibria depend on the solutions of a new set of cross-coupled stochastic algebraic Riccati equations (CSAREs). After establishing the asymptotic structure along with the positive semidefiniteness for the solutions of the CSAREs, a new sequential numerical algorithm and Newton´s method for solving the CSAREs are described. The resulting numerical solution is used to develop the Nash strategy. The efficiency of the proposed algorithm is demonstrated by solving a numerical example for a practical megawatt-frequency control problem.