单防御者对抗多轮攻击者，优化捕获率的博弈策略研究
Multi-Attacker Single-Defender Target Defense in Conical Environments
- 基于捕获分布推导攻防双方均衡策略
- 数值模拟验证捕获率理论结果，成功率可预测
- 适合研究动态对抗博弈与智能决策系统的人参考
我们研究平面锥形环境中的目标防御问题，其中单个防御者需拦截一系列来袭攻击者。攻击者的目的是在不被防御者捕获的前提下突破目标边界。一旦当前攻击者突破目标或被捕获，下一个攻击者将从环境边界出发，以最大速度径向向目标移动。因此，防御者在本轮结束时的位置即为下一轮的初始位置。攻击者会采用兼顾当前及未来交锋的策略，且具备有限感知范围的传感器，可精确检测防御者是否在其感知范围内。通过捕获分布的概念，我们推导出所有参与方的均衡策略以最大化捕获率，并通过蒙特卡洛类型的随机实验验证了理论结果。
原文摘要 · Abstract (English)
We consider a variant of the target defense problem in a planar conical environment where a single defender is tasked to capture a sequence of incoming attackers. The attackers' objective is to breach the target boundary without being captured by the defender. As soon as the current attacker breaches the target or gets captured by the defender, the next attacker appears at the boundary of the environment and moves radially toward the target with maximum speed. Therefore, the defender's final location at the end of the current game becomes its initial location for the next game. The attackers pick strategies that are advantageous for the current as well as for future engagements between the defender and the remaining attackers. The attackers have their own sensors with limited range, using which they can perfectly detect if the defender is within their sensing range. We derive equilibrium strategies for all the players to optimize the capture percentage using the notions of capture distribution. Finally, the theoretical results are verified through numerical examples using Monte Carlo type random trials of experiments.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。