High-Order approximation of soft constrained nash strategy for weakly coupled large-scale systems

In this paper, a high-order soft constrained Nash strategy for weakly coupled large-scale systems is investigated. In order to solve the cross-coupled sign-indefinite algebraic Riccati equations (CSAREs) that results in such strategy, the iterative algorithm that is based on the Newton´s method is applied. Using these iterative solutions, a high-order soft constrained Nash strategy is designed. As a result, it is proved that the proposed high-order approximate equilibrium strategies achieve better performance. Finally, in order to demonstrate the efficiency of the algorithm, a numerical example is given.