Infinite-horizon soft-constrained stochastic Nash games with state-dependent noise in weakly coupled large-scale systems

In this paper, we discuss infinite-horizon soft- constrained stochastic Nash games involving state-dependent noise in weakly coupled large-scale systems. First, linear quadratic differential games are formulated in which robustness is attained against model uncertainty. In particular, conditions for the existence of robust equilibria have been derived from the solutions of the sets of cross-coupled stochastic algebraic Riccati equations (CSAREs) for the first time. After establishing an asymptotic structure along with positive semidefiniteness for CSARE solutions, we derive a new algorithm based on Lyapunov iterations for solving the CSAREs. Consequently, we show that the proposed algorithm attains linear convergence and reduced-order computations for a sufficiently small value of e. Finally, numerical example is provided to verify the efficiency of the proposed algorithm.