论文标题
用附带的防守者守护翻译线
Guarding a Translating Line with an Attached Defender
论文作者
论文摘要
在本文中，我们考虑了一个目标保护差异游戏，在该游戏中，防守者必须通过拦截试图达到它的攻击者来保护线性移动的线段。与常见的目标保护问题相反，我们假设防御者附着在目标上并随之移动。此假设会根据其标题方向影响防守者的最大速度。研究了赢得攻击者方案的零和差分游戏，其中将回报定义为达到目标时两个代理商之间的距离。我们通过利用解决方案的无限长度目标情景来得出平衡策略和价值函数。此值函数的零级集合提供了将状态空间划分为防御者赢得和攻击者获奖区域的屏障表面。我们在结束时提出了模拟结果，以证明理论结果。
In this paper we consider a Target-guarding differential game where the Defender must protect a linearly moving line segment by intercepting the Attacker who tries to reach it. In contrast to common Target-guarding problems, we assume that the Defender is attached to the Target and moves along with it. This assumption affects the Defender's maximum speed depending on its heading direction. A zero-sum differential game of degree for the Attacker-winning scenario is studied, where the payoff is defined to be the distance between the two agents at the time of reaching the Target. We derive the equilibrium strategies and the Value function by leveraging the solution for the infinite-length Target scenario. The zero-level set of this Value function provides the barrier surface that divides the state space into Defender-winning and Attacker-winning regions. We present simulation results at the end to demonstrate the theoretical results.
