论文标题
在不同尺寸的空间中具有不同速度的玩家的追求逃避差异游戏
Pursuit-evasion differential games of players with different speeds in spaces of different dimensions
论文作者
论文摘要
我们研究了更快的追求者在3D空间中移动的追求差异游戏和在飞机上移动的逃生者。我们首先将著名的Apollonius圆圈扩展到3D空间，通过该空间，我们为被考虑的两个玩家构造了等速线。然后，考虑有和没有静态目标的两个情况，并使用等音等级的概念得出了相应的最佳策略。为了确保提出的策略的最佳性，给出了价值函数，并进一步证明是汉密尔顿 - 雅各布 - 伊斯兰公式的解决方案。进行了拟议策略与其他经典策略之间的比较，结果表明了拟议策略的最佳性。
We study pursuit-evasion differential games between a faster pursuer moving in 3D space and an evader moving in a plane. We first extend the well-known Apollonius circle to 3D space, by which we construct the isochron for the considered two players. Then both cases with and without a static target are considered and the corresponding optimal strategies are derived using the concept of isochron. In order to guarantee the optimality of the proposed strategies, the value functions are given and are further proved to be the solution of Hamilton-Jacobi-Isaacs equation. Simulations with comparison between the proposed strategies and other classical strategies are carried out and the results show the optimality of the proposed strategies.
