主动目标防御的完全微分对策
The Complete Differential Game of Active Target Defense
摘要：
在目标-攻击者-防御者（Target-Attacker-Defender，简称A-D）微分对策中，攻击者导弹试图捕获目标飞机。目标试图逃离攻击者，并得到防御者导弹的帮助，该导弹旨在在攻击者成功接近目标之前拦截攻击者。这些智能对手之间的冲突已被适当地建模为零和微分对策。最优策略已被合成，覆盖目标/防守方团队能够赢得比赛的状态空间的区域。然而，在攻击者的胜利区域的程度的游戏还没有得到充分的解决。设计参与者策略的初步尝试在微分对策意义上并没有被证明是最优的。本文的主要结果给出了在状态空间中攻击者获胜区域内度博弈的最优策略。证明了所得到的策略提供了博弈的鞍点解;得到了价值函数，并证明了它是连续的和连续可微的。它也证明了它是Hamilton-Jacobi-Isaacs（HJI）方程的解。最后，将所得策略与文献[22]中的解微分微分对策的最新结果进行了比较。通过反例证明了文[22]中提出的策略不是最优的。本文合成并验证了这个微分对策的唯一正则解，它实际上提供了一个半透屏障面。
英文摘要：
In the Target-Attacker-Defender (TAD) differential game, an Attacker missile strives to capture a Target aircraft. The Target tries to escape the Attacker and is aided by a Defender missile which aims at intercepting the Attacker before the latter manages to close in on the Target. The conflict between these intelligent adversaries has been suitably modeled as a zero-sum differential game. Optimal strategies have been synthesized covering the region of the state space where the Target/Defender team is able to win the game. However, the Game of Degree in the Attacker's region of win has not been fully addressed. Preliminary attempts at designing the players' strategies have not been proven to be optimal in the differential game sense. The main results of the paper present the optimal strategies of the Game of Degree in the Attacker's winning region of the state space. It is proven that the obtained strategies provide the saddle-point solution of the game; the Value function is obtained and it is shown to be continuous and continuously differentiable. It is also demonstrated that it is the solution of the Hamilton-Jacobi-Isaacs (HJI) equation. Finally, the obtained strategies are compared to recent results addressing the TAD differential game in [22]. It is shown by counterexample that the strategies proposed in [22] are not optimal. The unique regular solution of this differential game that actually provides a semipermeable Barrier surface is synthesized and verified in this paper.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
