TITLE:
Optimal Strategies in a Line Target Reach-Avoid Differential Game
AUTHORS:
Xinyi Zhu, Yan Zhu, Fangfei Li
KEYWORDS:
Differential Game, Pursuit-Evasion, Reach-Avoid, Optimal Control, Target Line
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.11,
November
20,
2025
ABSTRACT: This study investigates a planar differential game involving a singular attacker and defender, wherein the attacker endeavors to arrive at a specified target line while the defender seeks to intercept prior to this occurrence. The game is formulated with explicit boundary conditions, and the derivation of optimal strategies for both participants is conducted by examining the geometric characteristics of the reachable sets and terminal configurations. In contrast to traditional pursuit-evasion games, which utilize point or circular targets, the introduction of a target line presents unique geometric intricacies that complicate the determination of interception conditions. Analytical solutions for optimal controls are derived, accompanied by a lucid geometric interpretation of terminal states. The proposed formulation not only broadens the reach-avoid framework to encompass line-type targets but also offers theoretical guidance for practical defense scenarios involving extended boundaries. Ultimately, the analysis of this simplified single-attacker-single-defender scenario provides a foundational basis for future explorations into multi-agent defense systems.