Linear Pursuit-Evasion Games and the Isotropic Rocket

Abstract : The document is primarily a study of linear pursuit-evasion games, although several concepts and results are presented that apply to any zero-sum two-person differential game. The direct method of Pontryagin, specifically dealing with linear pursuit-evasion games, is presented and discussed. It is shown how it applies to several information structures. An interesting question is that of the optimality of the strategies generated. It turns out to be closely related to the continuous limit of the discretized information structure used, and of the induced epsilon-strategies.