Convergence proof for recursive solution of linear-quadratic Nash games for quasi-singularly perturbed systems

Abstract

A recursive method for the solution of the Riccati equations that yield the matrix gains required for the Nash strategies for quasi-singularly perturbed systems is presented. This method involves solution of Lyapunov and reduced-order Riccati equations corresponding to reduced-order fast and slow subsystems. The algorithm is shown to converge, under specified assumptions, to the exact solution with error at the kth iteration being O(epsilon(k)) where epsilon is a small, positive, singular perturbation parameter.