Approximate solutions to a class of nonlinear differential games using a shared dynamic extension

A class of nonzero-sum differential games is considered and a dynamic state feedback control law that approximates the solution of the differential game is proposed. The control law relies upon the solution of algebraic equations in place of partial differential equations or inequalities and makes use of dynamics shared by the players, thus relaxing the structural assumption required in [1]. The idea is firstly illustrated by the two-player case and then extended to the N-player case. A simple numerical example completes the paper.