炮塔逃生微分对策

IF 1.1 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Alexander Von Moll, Zachariah Fuchs, Daigo Shishika, Dipankar Maity, Michael Dorothy, Meir Pachter
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引用次数: 0

摘要

本文建立并求解了一个零和微分博弈,其中一个移动的逃兵试图从一个原点有一个静止的、有回合约束的炮塔的圆内逃跑。这个场景是著名的“湖中淑女”游戏的一个变体,在这个游戏中,受海岸限制的追击者被炮塔取代。与前者一样,假设炮塔的最大角速度大于规避器的线速度。因为有两种可能的结果,所以就产生了一种“同类游戏”——要么逃避者通过到达圆圈的周长而获胜,要么炮塔通过与后者的位置对齐而获胜。屏障表面将状态空间划分为两个区域,对应这两个结果,并在每个区域内求解一个度博弈。度博弈的解决方案由价值函数(即成本/效用的均衡值作为状态的函数)和两个参与者的鞍点均衡控制策略组成。就像湖上的女人一样,逃避者的平衡策略并不是唯一定义的,因为它比炮塔有角度速率优势。与《湖中女子》游戏不同的是,Evader的损失区域适用于所有速比,并且有一个额外的半渗透表面,将中心和岸边的Evader轨迹分开。解决方案在很大程度上取决于药剂的速比;特别地,有两种速比结构具有不同的溶液结构。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Turret escape differential game
In this paper, a zero-sum differential game is formulated and solved in which a mobile Evader seeks to escape from within a circle at whose origin lies a stationary, turn-constrained Turret. The scenario is a variant of the famous Lady in the Lake game in which the shore-constrained Pursuer has been replaced with the Turret. As in the former, it is assumed that the Turret's maximum angular rate is greater than the linear velocity of the Evader. Since two outcomes are possible, a Game of Kind arises - either the Evader wins by reaching the perimeter of the circle, or the Turret wins by aligning with the latter's position. A barrier surface partitions the state space into two regions corresponding to these two outcomes and a Game of Degree is solved within each region. The solutions to the Games of Degree are comprised of the Value functions (i.e., the equilibrium value of the cost/utility as a function of the state) and the saddle-point equilibrium control policies for the two players. Like the Lady in the Lake game, the equilibrium policy of the Evader is not uniquely defined where it has angular rate advantage over the Turret. Unlike the Lady in the Lake game, the losing region for the Evader is present for all speed ratios, and there is an additional semi-permeable surface separating center- and shore-bound Evader trajectories. The solution depends heavily upon the speed ratio of the agents; in particular, there are two speed ratio regimes with distinctive solution structures.
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来源期刊
Journal of Dynamics and Games
Journal of Dynamics and Games MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
2.00
自引率
0.00%
发文量
26
期刊介绍: The Journal of Dynamics and Games (JDG) is a pure and applied mathematical journal that publishes high quality peer-review and expository papers in all research areas of expertise of its editors. The main focus of JDG is in the interface of Dynamical Systems and Game Theory.
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