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, C1 and C2. The objective is to determine a point (u*,v*) in U × V, where U and V are the control spaces for C1 and C2, respectively, that satisfies an integral form of Pontryagin's maximum principle for differential games.