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

Abstract

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.