A differential dynamic programming algorithm for differential games

We develop and prove the convergence of a first‐order differential dynamic programming algorithm for the solution of a zero‐sum two‐person differential game with perfect information. The algorithm extends a first‐order strong variation algorithm for optimal control given by Mayne and Polak. Assuming separability of the Hamiltonian, we decompose the differential game problem into two control subproblems, C 1 and C 2 . The objective is to determine a point ( u * , v * ) in U × V , where U and V are the control spaces for C 1 and C 2 , respectively, that satisfies an integral form of Pontryagin's maximum principle for differential games. Copyright © 2001 John Wiley & Sons, Ltd.