具有逐点约束的追逃微分博弈的解与最优策略

中文摘要 AI 辅助

本研究探讨序列空间$l_2$中涉及可数多个追逃者$p_1,p_2,\boldsymbol{\rm K},p_m$和单个逃避者$e$且受逐点（几何）约束的追逃微分博弈。追逃者按指定的一阶微分方程演化，逃避者遵循二阶微分方程。博弈周期为长度$\theta$单位时间的固定时间区间。终端时刻逃避者与追逃者的最小距离表示博弈收益，追逃者旨在最小化该收益，逃避者则试图最大化它。我们得到了该博弈的解，包括参与者最优策略的构造以及博弈值估计。

英文摘要

This work study a differential game of pursuit-evasion involving countably many pursuers $p_{1},p_{2},\cdots,p_{m}$ and a single evader $e$ under point-wise (geometric) constraints in the sequence space $l_{2}.$ The pursuers evolve according to specified differential equations of $1^{st}$ order while the evader follows a $2^{nd}$ order differential equation. The game period is a fixed time interval of length $θ$ unit of time. The minimum distance between evader and the pursuer at the terminal time denotes the game payoff. The pursuers aim is to minimize the payoff, whereas the evader seeks to maximize it. We obtain the solution of the game, including optimal strategies of the players construction, as well as game value estimation.

发表机构

• Federal University Gashua（加舒瓦联邦大学）
• Bayero University Kano（卡诺拜鲁克大学）
• Kwantlen Polytechnics University（昆特兰理工大学）

机构由 AI 辅助整理，请以论文原文为准。