保护紧凸目标集的最优策略：微分对策方法
Optimal Strategies for Guarding a Compact and Convex Target Set: A Differential Game Approach
摘要：
我们重新审视最初由Isaacs提出的两人平面目标防御游戏，其中追击者（或防御者）试图保护目标集免受逃避者（或攻击者）的攻击。本文建立在现有的解析解的游戏，捍卫一个简单的形状的目标区开发一个广义和扩展的解决方案，同一个游戏的一个紧凑的凸目标集与光滑的边界。Isaacs的方法被应用于解决类博弈和度博弈。一个几何解决方案的方法是用来找到的障碍表面，划定获胜的球员集。一个价值函数加上一组最优状态反馈策略，在每个获胜的集合推导并证明对应于鞍点解的游戏。所提出的解决方案是通过数值模拟来说明。
英文摘要：
We revisit the two-player planar target-defense game initially posed by Isaacs where a pursuer (or defender) attempts to guard a target set from an attack by an evader (or attacker). This paper builds on existing analytical solutions to games of defending a simple shape of target area to develop a generalized and extended solution to the same game with a compact convex target set with smooth boundary. Isaacs' method is applied to address the game of kind and games of degree. A geometric solution approach is used to find the barrier surface that demarcates the winning sets of the players. A value function coupled with a set of optimal state feedback strategies in each winning set is derived and proven to correspond to the saddle point solution of the game. The proposed solutions are illustrated by means of numerical simulations.
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