发表机构
Georgia Institute of Technology; George Mason University; University of North Carolina at Charlotte; DEVCOM Army Research Laboratory（佐治亚理工学院; 乔治梅森大学; 北卡罗来纳大学夏洛特分校; DEVCOM陆军研究实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出基于集合的动态规划方法，为图上追逃博弈提供必要且充分的获胜条件，并转化为反馈策略，同时给出无法保证获胜状态下的获胜概率界限。
AI 中文摘要
本研究识别了离散、同时移动的图上追逃博弈的优势区域。现有的几何方法提供了获胜区域的有效刻画，但通常仅给出充分条件并依赖于开环策略。为应对这些挑战，我们开发了一种基于集合的动态规划方法来刻画追捕者的获胜与失败区域，在最坏情况行为下提供必要且充分的获胜条件。可达性分析具有集合追逐的解释，使得优势集合能够转化为实时适应玩家位置的反馈策略。对于双方都无法保证获胜的状态，我们引入了一种即时矩阵博弈公式，并建立了追捕者获胜概率的上下界。仿真结果验证了优势区域刻画及所提界限的正确性。
英文摘要
This work identifies the dominance regions for discrete, simultaneous-move pursuit-evasion games on graphs. Existing geometric approaches provide efficient characterizations of winning regions, but typically provide only sufficient conditions and rely on open-loop strategies. To address these challenges, we develop a set-based dynamic programming approach to characterize the pursuer's winning and losing regions, providing necessary and sufficient winning conditions under worst-case behavior. The reachability analysis admits a set-chasing interpretation, allowing translation of dominance sets to feedback strategies that adapt to the players' positions in real time. For states where neither player can guarantee victory, we introduce an instantaneous matrix-game formulation and establish upper and lower bounds on the pursuer's winning probability. Simulation results validate the correctness of the dominance-region characterization and the proposed bounds.
Comments7 pages, accepted at CDC 2026
