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Meeting	ACGS Committee Meeting 125 - Virtual - November 2020
Agenda Location	4 GENERAL COMMITTEE TECHNICAL SESSION 4.5 Sub-Committee D 4.5.1 Large-Scale Pursuit-Evasion Differential Games
Title	Large-Scale Pursuit-Evasion Differential Games
Presenter	David Casbeer
Affiliation	AFRL
Available Downloads*	presentation
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Abstract	Differential game theory provides the right framework to analyze pursuit evasion problems and, as a corollary, combat games. Pursuit-evasion scenarios involving multiple agents are important but challenging problems in aerospace, control, and robotics. Most pursuit-evasion differential games consider a small number of players due to the curse of dimensionality. We consider an N-pursuer vs. M-evader team conflict. This work extends classical differential game theory to simultaneously address weapon assignments and multi-player pursuit evasion scenarios. Saddle-point strategies that provide guaranteed performance for each team regardless of the actual strategies implemented by the opponent are devised. The players’ optimal strategies require the co-design of cooperative optimal assignments and optimal guidance laws. A representative measure of performance is proposed and the Value function of the game is obtained. It is shown that the Value function is continuous, continuously differentiable, and that it satisfies the Hamilton-Jacobi-Isaacs equation – the curse of dimensionality is overcome and the optimal strategies are obtained. The cases of N = M and N > M are considered. In the latter case, cooperative guidance strategies are also developed in order for the pursuers to exploit their numerical advantage. This work provides a foundation to formally analyze hybrid and high dimensional conflicts between teams of N pursuers and M evaders by means of differential game theory.