Numerical solutions of soft constrained nash games for multiparameter singularly perturbed systems

In this paper, the soft constrained Nash games for multiparameter singularly perturbed systems (MSPS) are discussed. After establishing the asymptotic structure and local uniqueness of the solution for the cross-coupled sign-indefinite multiparameter algebraic Riccati equations (CSMARE), a new algorithm that is based on Newton’s method for solving the CSMARE is established. As a result, it is shown that the proposed algorithm attains quadratic convergence. Moreover, in order to solve the cross-coupled multiparameter algebraic Lyapunov equation (CMALE) that appears in Newton’s method, a new gradient-based iterative algorithm is proposed.