A Successive Relaxation Approach for Solving the Coupled Hamilton–Jacobi–Isaacs Equations in Nonzero-Sum Differential Games of Affine Nonlinear Systems

Abstract

In this paper, we present a successive relaxation method for solving the coupled Hamilton–Jacobi–Isaacs equations (HJIEs) arising in non-zero sum differential-game of affine nonlinear systems. In particular, we consider the coupled-HJIEs arising in the mixed \({\mathcal {H}}_{2}/{\mathcal {H}}_{\infty }\) control problem, and establish convergence of the method under fairly mild assumptions. Examples are also presented to demonstrate the effectiveness of the method.