慢速防御者防御静态目标点
Defending a Static Target Point with a Slow Defender
AI总结：
本文研究慢速防御者与快速攻击者的目标防御博弈，通过分析三个博弈阶段和屏障曲面，提出保证攻防双方各自获胜的策略，并用数值实验验证其有效性。
摘要：
本文研究了一个由慢速防御者和快速攻击者之间的目标防御博弈。如果攻击者到达目标并避开防御者的捕获圆盘，则攻击者获胜。防御者通过阻止攻击者到达目标来获胜，这包括到达目标并将其包含在捕获圆盘中。根据初始条件，攻击者必须绕行防御者的捕获圆盘，导致轨迹受到约束。这一条件产生了博弈的三个阶段，我们对其进行分析以求解博弈的类型。我们提供了将状态空间划分为攻击者获胜区域和防御者获胜区域的屏障曲面，并给出了保证每个区域获胜的相应策略。数值实验证明了理论结果以及所提出策略的有效性。
英文摘要：
This paper studies a target-defense game played between a slow defender and a fast attacker. The attacker wins the game if it reaches the target while avoiding the defender's capture disk. The defender wins the game by preventing the attacker from reaching the target, which includes reaching the target and containing it in the capture disk. Depending on the initial condition, the attacker must circumnavigate the defender's capture disk, resulting in a constrained trajectory. This condition produces three phases of the game, which we analyze to solve for the game of kind. We provide the barrier surface that divides the state space into attacker-win and defender win regions, and present the corresponding strategies that guarantee win for each region. Numerical experiments demonstrate the theoretical results as well as the efficacy of the proposed strategies.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
