Singularities within a Dual-Evader Single-Pursuer Pursuit-Evasion Optimal Control Problem

Abstract

An optimal control problem consisting of a single pursuer and a defensive team of two evaders is examined. The pursuer's control strategy is fixed to always follow one of the evaders. The defensive team seeks to maximize a cost inflicted on the pursuer. Termination of engagement occurs when one or both of the evaders is within the capture radius of the pursuer. We derive the optimality conditions for the single capture of each evader and the simultaneous capture of both evaders. A dispersal surface is analytically derived before presenting a terminal singularity present in the case of simultaneous capture. Finally, we present a unique dispersal surface that exists between trajectories terminating in single capture and simultaneous capture.