带 有 时 间 与 探 测 约 束 的“到 达 -回 避”博 弈

Based on the classic lifeline game，this paper proposes a novel kind of reach-avoid game with time limit and detection range of the players，due to the fact that the operating time of the aircraft is generally limited and the detectors equipped have limited detection range. Via analyzing all the possible neutral terminal state sets and the Hamiltonian of the game，the forms of the defender’s and the attacker’s optimal strategies are provided. Using the optimal strategies and the constraints of the players，we obtain the accurate solution to the barrier of the original game and prove the correctness of the results via numerical simulations. The barrier acquired separates the game space into two disjoint winning regions related to different players，which provides a quick way of judging the game’s outcomes and gives the theoretical foundation for the strategy formulation of the aircraft participating in the combat.