Optimal Feedback Strategy of a Superior Evader Passing Between Two Pursuers

In many differential games, the optimal feedback strategies cannot be given explicitly, even if the optimal trajectories are known. This is the case in the game introduced by Hagedorn and Breakwell [1], where a faster evader has to cross the gap between two pursuers, which strive to capture it. The authors managed to integrate the optimal trajectories of this game analytically. Our previous paper validated their work by analyzing the underlying theory and integrating the trajectories numerically. Here we present a problem-specific numerical method for calculating optimal controls of the pursuers and evader in any state, thus calculating the optimal feedback strategies. The method relies on the numerical integration of trajectories and is computationally efficient such that it may be applied in real-time.