Soft-constrained stochastic Nash games for weakly coupled large-scale discrete-time systems

In this paper, we discuss infinite-horizon soft-constrained stochastic Nash games involving state-dependent noise and deterministic uncertainties in weakly coupled large-scale discrete-time systems. First, we formulate linear quadratic soft-constrained Nash games in which robustness is attained against external disturbance. Then, the conditions for the existence of robust equilibrium are derived based on the solutions of sets of the discrete version of cross-coupled stochastic algebraic Riccati equations (CSAREs). Moreover, various reliable features such as mean square stability are analyzed. After establishing an asymptotic structure along with positive definiteness for CSAREs solutions, we derive the recursive algorithm for solving CSAREs. Finally, we provide a numerical example to verify the efficiency of the proposed method.