Decoy-Assisted Evasion Against a Pure-Pursuit Pursuer: Analysis and Strategy Design

This letter investigates a three-agent pursuit-evasion problem involving a pursuer, an evader, and a mobile decoy. The decoy is equipped with a jamming device that conceals the exact location of the evader, and the evader must remain within a certain distance from the decoy for the concealment to be effective. The pursuer has access only to the real-time location of the decoy and employs a pure pursuit strategy toward it. We formulate this scenario as a state-constrained optimal control problem in which the evader-decoy coalition seeks to maximize the capture time through cooperative strategies. We first show that indefinite evasion for the evader is possible and construct an explicit evader-decoy cooperative strategy to achieve it. We then establish sufficient conditions for guaranteed finite-time capture and derive an upper bound on the capture time. Numerical simulations validate the effectiveness of the proposed methodologies.