Synthesis of Optimal Strategies for Differential Games by Neural Networks

The paper deals with the numerical approximation of optimal strategies for two-person zero-sum differential games of pursuit-evasion type by neural networks. Thereby, the feedback strategies can be computed in real-time after the training of appropriate neural networks. For this purpose, sufficiently many optimal trajectories and their associated openloop representations of the optimal feedback strategies must be computed, to provide data for training and cross-validation of the neural networks. All the precomputations can be carried through in a highly parallel way. This approach turns out to be applicable for differential games of more general type. The performance of the method is demonstrated for a modified cornered rat game where a pursuing cat and an evading rat, both moving in simple motion, are constrained to a rectangular arena. Two holes in the walls surrounding the arena enable the rat to evade once and for all, if the rat is not too far from these holes. The optimal traject..