Improved methods to solve the stochastic Nash games for weakly coupled large-scale systems iteratively

摘要

In this paper, the stochastic Nash games for weakly coupled large-scale systems with state-dependent noise are considered. The considered stochastic algebraic Riccati equations are quite different from the existing results in the sense that the equations have the additional linear term. The numerical algorithm based on the Newton method for solving the set of cross-coupled stochastic algebraic Riccati equations is derived by Mukaidani (Automatica 45(2009) 1272-1279). We modify this iteration and propose two new recursive equations with linear rate of convergence solving the considered set of Riccati equations. We carry out numerical experiments to illustrate the effectiveness of the considered iterations.