带有时间与探测约束的“到达-回避”博弈

Reach-avoid game with time limit and detection range

针对飞行器具有运行时间约束以及所携带探测器具有有限探测范围的现实情况,在传统生命线对策问题的基础上提出了一类考虑时间约束与探测约束的新型“到达-回避”定性微分对策博弈。通过分析对策问题所有可能的中性终端集以及问题对应的哈密顿方程,给出了防御者与进攻者最优博弈策略形式。利用所得到的策略和攻防双方的约束条件,得到了原问题对应界栅的精确解,并通过数值仿真验证了界栅的正确性。所得到的界栅可将博弈空间分为攻防双方的获胜区域,并可用于快速判断博弈问题最终结果,为飞行器攻防博弈双方的策略制定提供理论依据。

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 de⁃tectors equipped have limited detection range.Via analyzing all the possible neutral terminal state sets and the Hamil⁃tonian 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.