论文标题
使用附带的防御者守护非节能的翻译线
Guarding a Non-Maneuverable Translating Line with an Attached Defender
论文作者
论文摘要
在本文中，我们考虑了一种防护目标差异游戏，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翻译线段。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。此假设会影响捍卫者在惯性框架中的最大速度，这取决于目标的运动方向。研究了攻击者赢家和防守球场的零和差异游戏，其中都被研究了，在比赛终止时，收益定义为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守者获胜和攻击者获胜区域的屏障表面。我们提出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 translating line-segment by intercepting an 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 defenders' maximum speed in inertial frame, which depends on the target's direction of motion. Zero-sum differential game of degree for both the attacker-win and defender-win scenarios are studied, where the payoff is defined to be the distance between the two agents at the time of game termination. 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-win and attacker-win regions. We present simulation results to demonstrate the theoretical results.
