Numerical algorithm for solving cross-coupled algebraic Riccati equations related to Nash games of multimodeling systems

In this paper, the numerical design of a Nash equilibrium for infinite horizon multiparameter singularly perturbed systems (MSPS) is analyzed. A new algorithm which is based on the Newton method for solving the generalized cross-coupled multiparameter algebraic Riccati equations (GCMARE), is proposed. It is proven that the proposed algorithm guarantees the quadratic convergence. As a result, it is shown the proposed algorithm succeed in improving the convergence rate dramatically compared with the existing results.