Minimax algorithm for constructing an optimal control strategy in differential games with a lipschitz payoff

For a zero-sum differential game, an algorithm is proposed for computing the value of the game and constructing optimal control strategies with the help of stepwise minimax. It is assumed that the dynamics can be nonlinear and the cost functional of the game is the sum of an integral term and a terminal payoff function that satisfies the Lipschitz condition but can be neither convex nor concave. The players' controls are chosen from given sets that are generally time-dependent and unbounded. An error estimate for the algorithm is obtained depending on the number of partition points in the time interval and on the fineness of the spatial triangulation. Numerical results for an illustrative example are presented.