Efficient Numerical Computations of Soft Constrained Nash Strategy for Weakly Coupled Large-Scale Systems

Abstract

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) corresponding to strategy, the iterative algorithm on the basis of the Newton’s method is first applied. Second, the recursive algorithm for solving the CSAREs is also established to reduce the amount of algebraic computation as compared with the Newton’s method. Using these iterative solutions, a highorder 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.