Singular Solutions of the Optimal Pursuer Response to Fixed Control Strategies of a Dual-Evader Defensive Team

The optimal pursuer response to fixed evader control strategies within a single-pursuer, dual-evader engagement is examined. The evaders inflict a cost on the pursuer during the engagement based on the relative geometry of the three-agent system, and the pursuer strives to minimize the total accumulated cost over the duration of the engagement. Three possible termination cases are presented, and unique optimality conditions are examined for each. Singularities are then discussed, which include a singularity in the case of simultaneous capture and an analytically proven dispersal surface. We conclude by presenting a pair of unique dispersal surfaces and highlight the effect the solutions emanating from these surfaces have on their resultant value functions.