Cooperative defense within a single-pursuer, two-evader pursuit evasion differential game

This paper is motivated by a desire to develop analytical formulations for cooperative defensive strategies against predator(s).We formulate a single-pursuer, two-evader differential game with a novel cost functional. Each of the three agents are modeled as massless particles that move with constant velocity. The pursuer attempts to capture either of the evaders while minimizing its cost. Simultaneously, the evaders strive to maximize the pursuer's cost. The proposed cost functional represents the increased cost to the pursuer when presented with multiple, potentially dangerous targets. It captures the effect of cooperation between the evaders. In order to solve the game, we develop the optimality conditions for the equilibrium strategies. We then integrate the resulting system of ordinary differential equations backwards in time from the terminal conditions to generate the optimal trajectories of the three agent system. The resulting trajectories display cooperative behaviors between the two evaders, which are qualitatively similar to behaviors found in predator-prey interactions in nature. Brief description of singular surfaces is also included.