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针对空中拦截机动目标在追逃博弈领域的挑战，深入研究了三维空间高速交会的三弹拦截机动目标的惯性运动追逃博弈。根据高速交会的运动特性，三个拦截弹分别存在三个固定交会时刻，与目标弹的距离达到最小，三维问题简化为具有固定终端时刻的平面问题。采用了一种有效的增强方法，确保支付函数全局连续可微，进而通过Hamilton-Jacobi-Isaacs方程推导纳什均衡策略的解析解。结果显示，拦截弹应采取沿恒定加速度方向进行拦截的策略，且该方向与固定交会时刻其指向目标弹位置的方向一致；目标弹则需不断调整其加速度方向以最大化逃脱机会，该结果可为三弹拦截机动目标的追逃博弈提供重要的策略指导。
Abstract：In response to the challenges in the field of pursuit-evasion games for aerial interception of maneuvering targets, an in-depth study is conducted on the inertial motion pursuit-evasion game involving three interceptors intercepting a maneuvering target during high-speed encounters in three-dimensional space. Based on the motion characteristics of high-speed encounters, three fixed encounter moments exist for three interceptors, respectively, at which the distance to the target missile reaches a minimum, and the three-dimensional problem is simplified to a planar problem with fixed terminal moments. An effective angmentation method is adopted to ensure the global continuity and differentiability of the payoff function, and then the analytical solution of the Nash equilibrium strategy is derived through the Hamilton-Jacobi-Isaacs equation. The research results indicate that the interceptors should adopt an interception strategy along a constant acceleration direction, which is consistent with the direction pointing to the target missile's position at the fixed encounter moment. The target missile needs to continuously adjust its acceleration direction to maximize the escape opportunity. These results provide a important strategic instruction for the pursuit-evasion game of three interceptors intercepting a maneuvering target.
[1]张凯杰，林浩申，夏冰.导弹集群智能突防技术的新发展[J].战术导弹技术，2018(5):1-5+44.
[2] Weintraub I E,Pachter M,Garcia E. An introduction to pursuit-evasion differential games[C]. The 2020American Control Conference(ACC),Chicago,USA,June 28-30,2020.
[3]骆帅，查旭，陆红.高速打击武器突防技术综述[J].战术导弹技术，2023(5):1-9.
[4] Ba?ar T,Zaccour G. Handbook of dynamic game theory[M]. Switzerland:Springer,2018.
[5] Kumkov S S,Patsko V S,Shinar J. On level sets with"narrow throats"in linear differential games[J]. International Game Theory Review,2005,7(3):285-311.
[6] Ganebny S A,Kumkov S S,Le Ménec S,et al. Model problem in a line with two pursuers and one evader[J].Dynamic Games and Applications,2012,2:228-257.
[7] Kumkov S,Patsko V,Le Ménec S. Game with two pursuers and one evader:Case of weak pursuers[J]. Advances in Dynamic Games:Theory,Applications,and Numerical Methods,2013,13:263-293.
[8] Zhang P F,Zhang Y Q. Two-step stackelberg approach for the two weak pursuers and one strong evader closed loop game[J]. IEEE Transactions on Automatic Control,2024,69(2):1309-1315
[9] Bakolas E,Tsiotras P. Optimal pursuit of moving targets using dynamic voronoi diagrams[C]. The 49th IEEE Conference on Decision and Control(CDC),Atlanta,Georgia,USA,December 15-17,2010.
[10] Makkapati V R,Kothari M. A cooperative pursuit strategy for a high-speed evader[C]. The AIAA Guidance,Navigation, and Control Conference, Diego, California,USA,January 4-8,2016.
[11] Pachter M,Von Moll A,Garcia E,et al. Two-on-one pursuit[J]. Journal of Guidance,Control,and Dynamics,2019,42(7):1638-1644.
[12] Pachter M. Isaacs’ two-on-one pursuit-evasion game[C]. The 18th International Symposium on Dynamic Games and Applications, Grenoble, France, July 9-12,2018.
[13] Jansson O,Harris M W. A geometrical,reachable set approach for constrained pursuit-evasion games with multiple pursuers and evaders[J]. Aerospace, 2023,10(5):477.
[14]苏昂.边界防御追逃微分博弈模型及其逆向方法[D].青岛：青岛大学，2023.
[15] Pashkov A,Terekhov S. A differential game of approach with two pursuers and one evader[J]. Journal of Optimization Theory and Applications,1987,55:303-311.
[16] Shinar J, Glizer V Y, Turetsky V. A pursuit-evasion game with hybrid pursuer dynamics[J]. European Journal of Control,2009,15(6):665-684.
[17] Ahmed I,Kumam P,Ibragimov G,et al. An optimal pursuit differential game problem with one evader and many pursuers[J]. Mathematics,2019,7(9):842.
[18] Salimi M,Ferrara M. Differential game of optimal pursuit of one evader by many pursuers[J]. International Journal of Game Theory,2019,48(2):481-490.
[19] Zhang Y Q, Zhang P F, Wang X D, et al. A payoff augmentation approach to two pursuers and one evader inertial model differential game[J]. IEEE Transactions on Aerospace and Electronic Systems,2022,59(2):1371-1381.
[20] Sz?ts J,Harmati I. Optimal strategies of a pursuit-evasion game with three pursuers and one superior evader[J]. Robotics and Autonomous Systems, 2023, 161(7):104360.
[21]陈灿，莫雳，郑多，等.非对称机动能力多无人机智能协同攻防对抗[J].航空学报，2020,41(12):342-354.
[22]崔雅萌，王会霞，郑春胜，等.高速飞行器追逃博弈决策技术[J].指挥与控制学报，2021,7(4):403-414.
[23]赵亮博，朱广生，张耀，等.智能飞行器追逃博弈中的关键技术及发展趋势[J].飞航导弹，2021(12):134-139.
[24]袁斐然，刘春生，陈必露.基于自适应动态规划的多对一追逃博弈策略[J].电光与控制，2022,29(1):1-6.
[25]王若冰，王晓芳.一种结合MADDPG和对比学习的无人机追逃博弈方法[J].宇航学报，2024,45(2):262-272.
[26] Liu Y F,Qi N M,Tang Z W. Linear quadratic differential game strategies with two-pursuit versus single-evader[J]. Chinese Journal of Aeronautics,2012,25(6):896-905.
Basic Information:
DOI：10.16358/j.issn.1009-1300.20240036
China Classification Code:TJ765
Citation Information:
[1]詹紫怡,张鹏飞,张奕群.三弹协同拦截机动目标惯性博弈研究[J].战术导弹技术,2025,No.232(04):133-140.DOI:10.16358/j.issn.1009-1300.20240036.
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