Singular Dispersal Solutions for a Multi-Agent Differential Game with Angle-Based Cost Function

The differential game between a single pursuer and a team of two evaders is examined where the pursuer’s objective is to terminate the game by capturing either of the evaders. The evaders seek to maximize an integral cost they impose upon the pursuer while the pursuer seeks to minimize the imposed integral cost. During the engagement, the instantaneous cost is based on the relative geometry of the system and incentivizes the evaders to flank the pursuer. The pursuer is able to mitigate the instantaneous cost through its direction of focus. All agents move with simple motion. We formulate the differential game, derive the regular equilibrium conditions, and perform the singular analysis for two dispersal surfaces within the global solution of the game. Illustrative examples of equilibrium state trajectories are provided for each of the dispersal surfaces that show the qualitative differences in behaviors for the pairs of dispersal solutions.