Abstract
This paper discusses the dynamic games for a class of discrete time weakly coupled large-scale stochastic systems. First, it is shown that Pareto and Nash strategy set can be designed by solving the cross-coupled stochastic discrete algebraic Riccati equations (CSDAREs). After establishing the asymptotic structure for these solutions of CSDAREs, weak coupling parameter independent strategy sets are given for their problems respectively. It is shown for the first time that these parameter-independent strategy sets are the same and the proposed strategy sets attain the Pareto suboptimarity and the approximate Nash equilibrium. In fact, it is proved that these strategy sets achieve O(ε2) approximation for all cost performances. Furthermore, it is worth pointing out that the proposed approximate strategy sets can be constructed by solving the parameter independent reduced-order discrete algebraic Riccati equations (DAREs) via LMI. As a result, the suboptimality of overall cost for each subsystem can be attained. Finally, in order to demonstrate the efficiency of the proposed design method, a numerical example is provided.
