论文标题
两辆汽车游戏的特定案例的时间 - 最佳反馈控制
A time-optimal feedback control for a particular case of the game of two cars
论文作者
论文摘要
在本文中，提出了对两辆汽车游戏的时间反馈解决方案，因为提出了追随者比逃避者更快，更敏捷的情况。引入了可触及套件的连续子集的概念，以表征反馈策略下时间最佳的追求远景游戏。使用这些子集，表明，如果最初的追随者与逃避者足够遥远，那么追随者和逃避者的反馈鞍点策略都与一个常见的切线相吻合。使用几何形状，可以确定四个可行的切线，并通过在每一个瞬间求解$ 2 \ times 2 $矩阵游戏来得出追求者的反馈Min-Max策略，而逃避者的最大最大策略则得出。使用拟议的反馈控制定律评估追求者和逃避者的输入，涉及微不足道的计算工作，因此适用于实时实施。通过将所得轨迹与使用数值技术求解差异游戏获得的轨迹进行比较，进一步验证了拟议的法律。
In this paper, a time-optimal feedback solution to the game of two cars, for the case where the pursuer is faster and more agile than the evader, is presented. The concept of continuous subsets of the reachable set is introduced to characterize the time-optimal pursuit-evasion game under feedback strategies. Using these subsets it is shown that, if initially the pursuer is distant enough from the evader, then the feedback saddle point strategies for both the pursuer and the evader are coincident with one of the common tangents from the minimum radius turning circles of the pursuer to the minimum radius turning circles of the evader. Using geometry, four feasible tangents are identified and the feedback min-max strategy for the pursuer and the max-min strategy for the evader are derived by solving a $2 \times 2$ matrix game at each instant. Insignificant computational effort is involved in evaluating the pursuer and evader inputs using the proposed feedback control law and hence it is suitable for real-time implementation. The proposed law is validated further by comparing the resulting trajectories with those obtained by solving the differential game using numerical techniques.
