We consider a variant of pursuit-evasion games where a single defender is tasked to defend a static target from a sequence of periodically arriving intruders. The intruders' objective is to breach the boundary of a circular target without being captured and the defender's objective is to capture as many intruders as possible. At the beginning of each period, a new intruder appears at a random location on the perimeter of a fixed circle surrounding the target and moves radially towards the target center to breach the target. The intruders are slower in speed compared to the defender and they have their own sensing footprint through which they can perfectly detect the defender if it is within their sensing range. Considering the speed and sensing limitations of the agents, we analyze the entire game by dividing it into partial information and full information phases. We address the defender's capturability using the notions of engagement surface and capture circle. We develop and analyze three efficient strategies for the defender and derive a lower bound on the capture fraction. Finally, we conduct a series of simulations and numerical experiments to compare and contrast the three proposed approaches.

翻译：我们研究追逃博弈的一种变体：单个防御者需保护一个静态目标，抵御周期性到达的入侵者序列。入侵者的目标是突破圆形目标边界而不被捕获，防御者的目标是尽可能多地捕获入侵者。在每个周期开始时，新入侵者出现在围绕目标的固定圆环周界随机位置，并径向朝目标中心移动以突破目标。入侵者速度低于防御者，且拥有自己的感知范围——当防御者进入该范围时，可被完全探测。考虑智能体的速度与感知限制，我们将整个博弈划分为部分信息与完全信息两个阶段进行分析。利用交界面与捕获圆概念，我们研究了防御者的可捕获性。针对防御者提出并分析了三种高效策略，推导出捕获比例的下界。最后通过系列仿真与数值实验对比评估了三种方法。