飞行器集群协同制导新进展

吕金虎; 于江龙; 董希旺

doi:10.16383/j.aas.c240499

飞行器集群协同制导新进展

doi: 10.16383/j.aas.c240499 cstr: 32138.14.j.aas.c240499

吕金虎^1,,
于江龙^1,,
董希旺^{1, 2, 3,}

1.
北京航空航天大学自动化科学与电气工程学院北京 100191
2.
北京航空航天大学无人系统研究院北京 100191
3.
北京航空航天大学人工智能学院北京 100191

基金项目: 国家自然科学基金(62141604, U2241217, 62103016, 62473029)资助

详细信息

作者简介:
吕金虎：北京航空航天大学教授. 主要研究方向为复杂系统, 协同制导控制, 工业互联网, 大数据. E-mail: lvjinhu@buaa.edu.cn

于江龙：北京航空航天大学副教授. 主要研究方向为飞行器集群, 协同制导. 本文通信作者. E-mail: sdjxyjl@buaa.edu.cn

董希旺：北京航空航天大学教授. 主要研究方向为集群智能, 协同控制, 协同制导.E-mail: xwdong@buaa.edu.cn

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出版历程
- 收稿日期: 2024-07-12
- 网络出版日期: 2025-02-12
- 刊出日期: 2025-04-15

New Progress in Cooperative Guidance for Aircraft Swarm System

LÜ Jin-Hu^1
,,
YU Jiang-Long^1
,,
DONG Xi-Wang^{1, 2, 3
,}

1.
School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191
2.
Institute of Unmanned System, Beihang University, Beijing 100191
3.
Institute of Artificial Intelligence, Beihang University, Beijing 100191

Funds: Supported by National Natural Science Foundation of China (62141604, U2241217, 62103016, 62473029)

More Information

Author Bio:
LÜ Jin-Hu　Professor at Beihang University. His research interest covers complex systems, cooperative guidance and control, industrial internet, and big data

YU Jiang-Long　Associate professor at Beihang University. His research interest covers aircraft swarm system and cooperative guidance. Corresponding author of this paper

DONG Xi-Wang　Professor at Beihang University. His research interest covers swarm intelligence, cooperative control, and cooperative guidance

摘要

摘要: 协同制导是飞行器集群遂行协同任务中最关键的环节之一, 也是飞行器制导控制领域近年来最重要的研究方向之一. 协同制导经历了从简单约束到复杂约束、单一任务到复杂任务的发展过程. 首先, 从协同制导的发展历程和任务级别角度进行分类, 将现有协同制导方法概括为打击时间/角度约束下的协同制导、编队构型约束下的协同制导、角色和任务互补下的协同制导、博弈对抗条件下的协同制导等四类协同制导方法; 其次, 总结国内外学者对相关领域理论成果的最新进展, 从研究方法层面综述相关成果的优缺点和适用范围; 最后, 对协同制导领域的技术挑战与难点进行深入分析, 并对协同制导技术的未来发展进行前瞻性展望.
- 飞行器集群 /
- 协同制导 /
- 新进展 /
- 发展展望
Abstract: Cooperative guidance is one of the most critical links in the execution of cooperative tasks for aircraft swarm system, and is also one of the most important research directions in the field of aircraft guidance and control in recent years. Cooperative guidance has evolved from simple constraints to complex constraints, from single tasks to complex tasks. First, this paper classifies the cooperative guidance issues from the perspective of its development history and task level, summarizing existing cooperative guidance methods into four categories: Cooperative guidance under impact time/angle constraint, cooperative guidance under formation constraint, cooperative guidance under role and task complementarity, and cooperative guidance under game adversarial conditions. Second, the paper summarizes the latest progress in related fields theoretical results by domestic and foreign scholars, and reviews the advantages and disadvantages and applicable scope of related research methods from the perspective of research method. Finally, the paper conducts in-depth analysis of the technical challenges and difficulties in the field of cooperative guidance, and provides a forward-looking perspective on the future development of cooperative guidance technology.
- Aircraft swarm system /
- cooperative guidance /
- new progress /
- development prospects

HTML全文

图 1 飞行器集群协同制导发展历程

Fig. 1 Development process of aircraft swarm system cooperative guidance

下载: 全尺寸图片幻灯片

图 2 终端时空约束下的飞行器集群协同制导方法

Fig. 2 Cooperative guidance methods for aircraft swarm system under terminal spatio-temporal constraints

下载: 全尺寸图片幻灯片

图 3 编队构型约束下的飞行器集群编队协同制导方法

Fig. 3 Cooperative guidance methods for aircraft swarm system formation under formation configuration constraints

下载: 全尺寸图片幻灯片

图 4 角色和任务互补的飞行器集群协同制导方法

Fig. 4 Role- and mission-complementary methods for cooperative guidance of aircraft swarm system

下载: 全尺寸图片幻灯片

图 5 对抗条件下的飞行器集群协同博弈制导方法

Fig. 5 Cooperative game guidance methods for aircraft swarm system under adversarial conditions

下载: 全尺寸图片幻灯片

参考文献(94)

[1]	Yu W W, Chen G R, Lü J H. On pinning synchronization of complex dynamical networks. Automatica, 2009, 45(2): 429−435 doi: 10.1016/j.automatica.2008.07.016
[2]	Lü J H, Chen G R. A new chaotic attractor coined. International Journal of Bifurcation and Chaos, 2002, 12(3): 659−661 doi: 10.1142/S0218127402004620
[3]	Lü J H, Chen G R. A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE Transactions on Automatic Control, 2005, 50(6): 841−846 doi: 10.1109/TAC.2005.849233
[4]	Zhou J, Lu J A, Lü J H. Adaptive synchronization of an uncertain complex dynamical network. IEEE Transactions on Automatic Control, 2006, 51(4): 652−656 doi: 10.1109/TAC.2006.872760
[5]	向锦武, 董希旺, 丁文锐, 索津莉, 沈林成, 夏辉. 复杂环境下无人集群系统自主协同关键技术. 航空学报, 2022, 43(10): Article No. 527570 Xiang Jin-Wu, Dong Xi-Wang, Ding Wen-Rui, Suo Jin-Li, Shen Lin-Cheng, Xia Hui. Key technologies for autonomous cooperation of unmanned swarm systems in complex environments. Acta Aeronautica et Astronautica Sinica, 2022, 43(10): Article No. 527570
[6]	Jeon I S, Lee J I, Tahk M J. Impact-time-control guidance law for anti-ship missiles. IEEE Transactions on Control Systems Technology, 2006, 14(2): 260−266 doi: 10.1109/TCST.2005.863655
[7]	赵斌, 梁乐成, 蒋瑞民, 周军. 终端角度约束制导及制导控制一体化方法综述. 宇航学报, 2022, 43(5): 563−579 Zhao Bin, Liang Le-Cheng, Jiang Rui-Min, Zhou Jun. Review of guidance and integrated guidance and control methods under terminal angle constraints. Journal of Astronautics, 2022, 43(5): 563−579
[8]	温广辉, 周佳玲, 吕跃祖, 刘照辉, 吕金虎. 多导弹协同作战中的分布式协调控制问题. 指挥与控制学报, 2021, 7(2): 137−145 doi: 10.3969/j.issn.2096-0204.2021.02.0137 Wen Guang-Hui, Zhou Jia-Ling, Lü Yue-Zu, Liu Zhao-Hui, Lü Jin-Hu. Distributed coordination control in multi-missile cooperative tasks. Journal of Command and Control, 2021, 7(2): 137−145 doi: 10.3969/j.issn.2096-0204.2021.02.0137
[9]	赵建博, 杨树兴. 多导弹协同制导研究综述. 航空学报, 2017, 38(1): Article No. 020256 Zhao Jian-Bo, Yang Shu-Xing. Review of multi-missile cooperative guidance. Acta Aeronautica et Astronautica Sinica, 2017, 38(1): Article No. 020256
[10]	Zhou J L, Wu X J, Lü Y Z, Li X D, Liu Z H. Recent progress on the study of multi-vehicle coordination in cooperative attack and defense: An overview. Asian Journal of Control, 2022, 24(2): 794−809 doi: 10.1002/asjc.2685
[11]	唐钟南, 辛宏博, 王玉杰, 陈清阳, 王鹏, 杨希祥. 基于协调变量的多机协同打击制导方法与试验验证. 工程科学学报, 2022, 44(8): 1396−1405 Tang Zhong-Nan, Xin Hong-Bo, Wang Yu-Jie, Chen Qing-Yang, Wang Peng, Yang Xi-Xiang. Coordinated variable-based guidance method and experimental verification for multi-UAVs. Chinese Journal of Engineering, 2022, 44(8): 1396−1405
[12]	魏明英, 崔正达, 李运迁. 多弹协同拦截综述与展望. 航空学报, 2020, 41(S1): Article No. 723804 Wei Ming-Ying, Cui Zheng-Da, Li Yun-Qian. Review and future development of multi-missile coordinated interception. Acta Aeronautica et Astronautica Sinica, 2020, 41(S1): Article No. 723804
[13]	侯博, 宋建梅, 张春妍, 张民强. 带落角和时间约束的网络化导弹协同制导律. 兵工学报, 2016, 37(3): 431−438 doi: 10.3969/j.issn.1000-1093.2016.03.007 Hou Bo, Song Jian-Mei, Zhang Chun-Yan, Zhang Min-Qiang. Cooperative guidance law with impact angle and impact time constraints for networked missiles. Acta Armamentarii, 2016, 37(3): 431−438 doi: 10.3969/j.issn.1000-1093.2016.03.007
[14]	Zhou J L, Yang J Y. Distributed guidance law design for cooperative simultaneous attacks with multiple missiles. Journal of Guidance, Control, and Dynamics, 2016, 39(10): 2439−2447 doi: 10.2514/1.G001609
[15]	赵世钰, 周锐. 基于协调变量的多导弹协同制导. 航空学报, 2008, 29(6): 1605−1611 Zhao Shi-Yu, Zhou Rui. Multi-missile cooperative guidance using coordination variables. Acta Aeronautica et Astronautica Sinica, 2008, 29(6): 1605−1611
[16]	Tang J C, Zuo Z Y. Cooperative circular guidance of multiple missiles: A practical prescribed-time consensus approach. Journal of Guidance, Control, and Dynamics, 2023, 46(9): 1799−1813 doi: 10.2514/1.G007431
[17]	Wang P Y, Guo Y N, Ma G F, Lee C H, Wie B. New look-angle tracking guidance strategy for impact time and angle control. Journal of Guidance, Control, and Dynamics, 2022, 45(3): 545−557 doi: 10.2514/1.G006229
[18]	李斌, 林德福, 何绍溟, 白冰. 基于最优误差动力学的时间角度控制制导律. 航空学报, 2018, 39(11): Article No. 322215 Li Bin, Lin De-Fu, He Shao-Ming, Bai Bing. Time and angle control guidance law based on optimal error dynamics. Acta Aeronautica et Astronautica Sinica, 2018, 39(11): Article No. 322215
[19]	Zhao Q L, Dong X W, Liang Z X, Bai C, Chen J, Ren Z. Distributed cooperative guidance for multiple missiles with fixed and switching communication topologies. Chinese Journal of Aeronautics, 2017, 30(4): 1570−1581 doi: 10.1016/j.cja.2017.06.009
[20]	Kumar S R, Mukherjee D. Cooperative saLüo guidance using finite-time consensus over directed cycles. IEEE Transactions on Aerospace and Electronic Systems, 2020, 56(2): 1504−1514 doi: 10.1109/TAES.2019.2934675
[21]	Kang S, Wang J N, Li G, Shan J Y, Petersen I R. Optimal cooperative guidance law for saLüo attack: An MPC-based consensus perspective. IEEE Transactions on Aerospace and Electronic Systems, 2018, 54(5): 2397−2410 doi: 10.1109/TAES.2018.2816880
[22]	Erer K S, Tekin R. Impact time and angle control based on constrained optimal solutions. Journal of Guidance, Control, and Dynamics, 2016, 39(10): 2448−2454 doi: 10.2514/1.G000414
[23]	张钰清, 陈长风, 张扬, 于江龙, 董希旺, 任章. 带有时间约束的多飞行器协同轨迹规划. 工程科学学报, 2024, 46(9): 1554−1564 doi: 10.13374/j.issn2095-9389.2023.11.23.002 Zhang Yu-Qing, Chen Chang-Feng, Zhang Yang, Yu Jiang-Long, Dong Xi-Wang, Ren Zhang. Time-coordination entry trajectory planning for multihypersonic vehicles. Chinese Journal of Engineering, 2024, 46(9): 1554−1564 doi: 10.13374/j.issn2095-9389.2023.11.23.002
[24]	陈中原, 韦文书, 陈万春. 基于强化学习的多发导弹协同打击智能制导律. 兵工学报, 2021, 42(8): 1638−1647 doi: 10.3969/j.issn.1000-1093.2021.08.008 Chen Zhong-Yuan, Wei Wen-Shu, Chen Wan-Chun. Reinforcement learning-based intelligent guidance law for cooperative attack of multiple missiles. Acta Armamentarii, 2021, 42(8): 1638−1647 doi: 10.3969/j.issn.1000-1093.2021.08.008
[25]	金泽宇, 刘凯, 尹中杰, 王龙. 基于神经网络剩余时间模型的协同制导律设计. 战术导弹技术, 2021(4): 103−109 Jin Ze-Yu, Liu Kai, Yin Zhong-Jie, Wang Long. Impact time cooperation guidance law design based on time-to-go estimating model using neural network. Tactical Missile Technology, 2021(4): 103−109
[26]	Kim B S, Lee J G, Han H S. Biased PNG law for impact with angular constraint. IEEE Transactions on Aerospace and Electronic Systems, 1998, 34(1): 277−288 doi: 10.1109/7.640285
[27]	张保峰. 带打击角度约束的多导弹协同导引律设计 [硕士学位论文], 哈尔滨工业大学, 中国, 2013. Zhang Bao-Feng. Design of Multi-missile Cooperative Guidance Law With Attack Angle Constraint [Master thesis], Harbin Institute of Technology, China, 2013.
[28]	Jiang H, An Z, Yu Y N, Chen S S, Xiong F F. Cooperative guidance with multiple constraints using convex optimization. Aerospace Science and Technology, 2018, 79: 426−440 doi: 10.1016/j.ast.2018.06.001
[29]	刘子超, 王江, 何绍溟, 李宇飞. 基于预测校正的落角约束计算制导方法. 航空学报, 2022, 43(8): Article No. 325433 Liu Zi-Chao, Wang Jiang, He Shao-Ming, Li Yu-Fei. A computational guidance algorithm for impact angle control based on predictor-corrector concept. Acta Aeronautica et Astronautica Sinica, 2022, 43(8): Article No. 325433
[30]	张友安, 梁勇, 刘京茂, 孙玉梅. 基于轨迹成型的打击角度与时间控制. 航空学报, 2018, 39(9): Article No. 322009 Zhang You-An, Liang Yong, Liu Jing-Mao, Sun Yu-Mei. Trajectory reshaping based impact angle and time control. Acta Aeronautica et Astronautica Sinica, 2018, 39(9): Article No. 322009
[31]	Chen Y D, Wang J N, Shan J Y, Xin M. Cooperative guidance for multiple powered missiles with constrained impact and bounded speed. Journal of Guidance, Control, and Dynamics, 2021, 44(4): 825−841 doi: 10.2514/1.G005578
[32]	Lyu T, Li C J, Guo Y N, Ma G F. Three-dimensional finite-time cooperative guidance for multiple missiles without radial velocity measurements. Chinese Journal of Aeronautics, 2019, 32(5): 1294−1304 doi: 10.1016/j.cja.2018.12.005
[33]	刘子超, 王江, 何绍溟. 基于深度学习的时间角度控制制导律. 系统工程与电子技术, 2023, 45(11): 3579−3587 Liu Zi-Chao, Wang Jiang, He Shao-Ming. Time and angle control guidance law based on deep learning. Systems Engineering and Electronics, 2023, 45(11): 3579−3587
[34]	Sun J L, Long T. Event-triggered distributed zero-sum differential game for nonlinear multi-agent systems using adaptive dynamic programming. ISA Transactions, 2021, 110: 39−52 doi: 10.1016/j.isatra.2020.10.043
[35]	Long T, Cao Y, Sun J L, Xu G T. Adaptive event-triggered distributed optimal guidance design via adaptive dynamic programming. Chinese Journal of Aeronautics, 2022, 35(7): 113−127 doi: 10.1016/j.cja.2021.08.005
[36]	任章, 于江龙. 多临近空间拦截器编队拦截自主协同制导控制技术研究. 导航定位与授时, 2018, 5(2): 1−6 Ren Zhang, Yu Jiang-Long. Research on the autonomous cooperative guidance control for the formation interception of multiple near space interceptors. Navigation Positioning and Timing, 2018, 5(2): 1−6
[37]	Dong X W, Li Y F, Lu C, Hu G Q, Li Q D, Ren Z. Time-varying formation tracking for UAV swarm systems with switching directed topologies. IEEE Transactions on Neural Networks and Learning Systems, 2019, 30(12): 3674−3685 doi: 10.1109/TNNLS.2018.2873063
[38]	阎宏磊, 陆远, 郭杰, 唐胜景, 李响. 欠驱动高超滑翔飞行器集群协同编队控制方法. 空天防御, 2024, 7(1): 56−62 Yan Hong-Lei, Lu Yuan, Guo Jie, Tang Sheng-Jing, Li Xiang. Cluster cooperative formation control method for underactuated hypersonic vehicle. Air and Space Defense, 2024, 7(1): 56−62
[39]	王利楠, 温广辉, 伊枭剑. 状态约束下的多飞行器有限时间姿态一致性控制. 现代防御技术, 2024, 52(2): 124−131 Wang Li-Nan, Wen Guang-Hui, Yi Xiao-Jian. Finite-time attitude consensus control of multiple unmanned aerial vehicles under state constraints. Modern Defense Technology, 2024, 52(2): 124−131
[40]	吴险峰, 陈宝文, 孙经广. 带有避障约束的分布式导弹编队饱和控制器设计. 航天控制, 2024, 42(2): 3−9 doi: 10.3969/j.issn.1006-3242.2024.02.001 Wu Xian-Feng, Chen Bao-Wen, Sun Jing-Guang. Design of distributed missile formation saturation controller with obstacle avoidance constraints. Aerospace Control, 2024, 42(2): 3−9 doi: 10.3969/j.issn.1006-3242.2024.02.001
[41]	喻煌超, 曹粟, 彭羽凡, 王祥科. 面向机动飞行的固定翼无人机位姿跟踪控制. 控制理论与应用, 2023, 40(12): 2217−2224 Yu Huang-Chao, Cao Su, Peng Yu-Fan, Wang Xiang-Ke. Pose tracking control of fixed-wing unmanned aerial vehicle towards maneuvering flight. Control Theory and Applications, 2023, 40(12): 2217−2224
[42]	Yu J L, Dong X W, Li Q D, Lü J H, Ren Z. Distributed adaptive cooperative time-varying formation tracking guidance for multiple aerial vehicles system. Aerospace Science and Technology, 2021, 117: Article No. 106925 doi: 10.1016/j.ast.2021.106925
[43]	王肖, 郭杰, 唐胜景, 祁帅. 基于解析剖面的时间协同再入制导. 航空学报, 2019, 40(3): Article No. 322565 Wang Xiao, Guo Jie, Tang Sheng-Jing, Qi Shuai. Time-cooperative entry guidance based on analytical profile. Acta Aeronautica et Astronautica Sinica, 2019, 40(3): Article No. 322565
[44]	王培臣, 闫循良, 南汶江, 李新国. 考虑时间约束的近解析滑翔轨迹快速规划方法. 兵工学报, 2024, 45(7): 2294−2305 Wang Pei-Chen, Yan Xun-Liang, Nan Wen-Jiang, Li Xin-Guo. A rapid and near analytic planning method for gliding trajectory under time constraints. Acta Armamentarii, 2024, 45(7): 2294−2305
[45]	沈馨, 李响, 张后军, 郭宇恒, 刘旭. 一种无动力条件下的再入滑翔飞行编队制导方法. 飞行力学, 2023, 41(4): 74−80 Shen Xin, Li Xiang, Zhang Hou-Jun, Guo Yu-Heng, Liu Xu. A formation guidance method for reentry unpowered gliding flight. Flight Dynamics, 2023, 41(4): 74−80
[46]	李惠峰, 李昭莹. 高超声速飞行器上升段最优制导间接法研究. 宇航学报, 2011, 32(2): 297−302 Li Hui-Feng, Li Zhao-Ying. Indirect method of optimal ascent guidance for hypersonic vehicle. Journal of Astronautics, 2011, 32(2): 297−302
[47]	刘冬责. 多导弹协同制导与控制技术研究 [硕士学位论文], 北京理工大学, 中国, 2016. Liu Dong-Ze. Research on Multi-missile Cooperative Guidance and Control Technology [Master thesis], Beijing Institute of Technology, China, 2016.
[48]	王紫扬. 多约束协同制导及编队飞行方法研究 [硕士学位论文], 北京理工大学, 中国, 2018. Wang Zi-Yang. Research on Cooperative Guidance and Formation Flight With Multiple Constraints [Master thesis], Beijing Institute of Technology, China, 2018.
[49]	Hong H C, Maity A, Holzapfel F. Free final-time constrained sequential quadratic programming-based flight vehicle guidance. Journal of Guidance, Control, and Dynamics, 2021, 44(1): 181−189 doi: 10.2514/1.G004874
[50]	江涌, 王林波, 王蒙一. “群对群”协同对抗的规划与制导问题研究. 中国科学: 技术科学, 2024, 54(3): 377−390 Jiang Yong, Wang Lin-Bo, Wang Meng-Yi. Planning and guidance challenges in a “group-to-group” collaborative confrontation. Scientia Sinica Technologica, 2024, 54(3): 377−390
[51]	Yang L Y, Zhao G, Wu B B, Yan G R. Assembly sequence planning for aircraft component based on improved clashes matrix. Applied Mechanics and Materials, 2011, 88−89: 22−28 doi: 10.4028/www.scientific.net/AMM.88-89.22
[52]	Zhai J P, Yang J Y. An integrated cooperative guidance design for target assignment and simultaneous attack on multiple targets. International Journal of Control, 2024, 97(10): 2175−2188 doi: 10.1080/00207179.2023.2260006
[53]	肖惟, 于江龙, 董希旺, 李清东, 任章. 过载约束下的大机动目标协同拦截. 航空学报, 2020, 41(S1): Article No. 723777 Xiao Wei, Yu Jiang-Long, Dong Xi-Wang, Li Qing-Dong, Ren Zhang. Cooperative interception against highly maneuvering target with acceleration constraints. Acta Aeronautica et Astronautica Sinica, 2020, 41(S1): Article No. 723777
[54]	王翰, 姜吉祥, 程林, 梁海朝. 基于覆盖控制的多机动目标合围拦截制导方法. 飞行力学, 2024, 42(5): 64−71 Wang Han, Jiang Ji-Xiang, Cheng Lin, Liang Hai-Zhao. Cooperative encirclement guidance strategy for intercepting multiple maneuverable targets. Flight Dynamics, 2024, 42(5): 64−71
[55]	王少博, 郭杨, 王仕成, 刘志国, 张帅. 带有引诱角色的多飞行器协同最优制导方法. 航空学报, 2020, 41(2): Article No. 323402 Wang Shao-Bo, Guo Yang, Wang Shi-Cheng, Liu Zhi-Guo, Zhang Shuai. Cooperative optimal guidance method for multi-aircraft with luring role. Acta Aeronautica et Astronautica Sinica, 2020, 41(2): Article No. 323402
[56]	张帅, 郭杨, 王仕成. 带有引诱角色的有限时间协同制导方法. 宇航学报, 2018, 39(3): 308−317 Zhang Shuai, Guo Yang, Wang Shi-Cheng. Finite time cooperative guidance method with a lure role. Journal of Astronautics, 2018, 39(3): 308−317
[57]	于江龙, 董希旺, 李清东, 吕金虎, 任章. 拦截机动目标的分布式协同围捕制导方法. 航空学报, 2022, 43(9): Article No. 325817 Yu Jiang-Long, Dong Xi-Wang, Li Qing-Dong, Lü Jin-Hu, Ren Zhang. Distributed cooperative encirclement hunting guidance method for intercepting maneuvering target. Acta Aeronautica et Astronautica Sinica, 2022, 43(9): Article No. 325817
[58]	江涌, 王林波, 王蒙一, 宋勋, 安鹏飞, 于江龙. 基于覆盖理论的高速强机动目标协同围捕策略. 工程科学学报, 2024, 46(7): 1169−1178 Jiang Yong, Wang Lin-Bo, Wang Meng-Yi, Song Xun, An Peng-Fei, Yu Jiang-Long. Coverage-based cooperative encirclement strategy against high-speed and highly maneuvering targets. Chinese Journal of Engineering, 2024, 46(7): 1169−1178
[59]	Chen S W, Wang W, Fan J F. Three-dimensional piecewise cooperative guidance with smooth switching topology. Aerospace Science and Technology, 2024, 150: Article No. 109181 doi: 10.1016/j.ast.2024.109181
[60]	葛云鹏, 梁卓, 吕瑞, 涂海峰, 严大卫. 一种基于主从模式的无动力飞行器协同制导方法. 中国惯性技术学报, 2023, 31(4): 418−424 Ge Yun-Peng, Liang Zhuo, Lü Rui, Tu Hai-Feng, Yan Da-Wei. A cooperative guidance method for unpowered vehicle based on master-slave mode. Journal of Chinese Inertial Technology, 2023, 31(4): 418−424
[61]	Tan M H, Shen H. Three-dimensional cooperative game guidance law for a leader-follower system with impact angles constraint. IEEE Transactions on Aerospace and Electronic Systems, 2024, 60(1): 405−420 doi: 10.1109/TAES.2023.3325795
[62]	Yu J L, Dong X W, Li Q D, Lü J H, Ren Z. Task coupling based layered cooperative guidance: Theories and applications. Control Engineering Practice, 2022, 121: Article No. 105050 doi: 10.1016/j.conengprac.2021.105050
[63]	Zhao J B, Yang S X, Xiong F F. Cooperative guidance of seeker-less missile with two leaders. Aerospace Science and Technology, 2019, 88: 308−315 doi: 10.1016/j.ast.2019.03.036
[64]	张邦楚, 伍勋, 胡森, 朱威禹. 体系保障下无导引头高超声速导弹网络化协同制导技术. 战术导弹技术, 2023(5): 114−123 Zhang Bang-Chu, Wu Xun, Hu Sen, Zhu Wei-Yu. Networked collaborative guidance technology for hypersonic missiles without seeker under system support. Tactical Missile Technology, 2023(5): 114−123
[65]	陈维义, 何凡, 李逸源, 董海迪. 三体对抗中的主动防御鲁棒最优预测制导律研究. 北京理工大学学报, 2024, 44(6): 645−654 Chen Wei-Yi, He Fan, Li Yi-Yuan, Dong Hai-Di. Robust optimal predictive guidance law for active defense in three-body confrontation. Transactions of Beijing Institute of Technology, 2024, 44(6): 645−654
[66]	李毅. 二对二攻防对抗协同制导律研究 [硕士学位论文], 哈尔滨工业大学, 中国, 2022. Li Yi. Cooperative Guidance Law for Two-on-two Attack-defense Confrontation [Master thesis], Harbin Institute of Technology, China, 2022.
[67]	Tan Z W, Fonod R, Shima T. Cooperative guidance law for target pair to lure two pursuers into collision. Journal of Guidance, Control, and Dynamics, 2018, 41(8): 1687−1699 doi: 10.2514/1.G003357
[68]	杨广超, 周传睿, 邢文革. 海战场无人机集群与反舰导弹协同作战样式与反制策略研究. 战术导弹技术, 2024, 1(1): 141−149 Yang Guang-Chao, Zhou Chuan-Rui, Xing Wen-Ge. Research on the collaborative combat mode and countermeasures of UAV swarm and anti-ship missile in naval battlefield. Tactical Missile Technology, 2024, 1(1): 141−149
[69]	张龙, 傅学庆, 明晓. 空海一体化协同防空作战样式设计. 飞控与探测, 2024, 7(2): 51−56 Zhang Long, Fu Xue-Qing, Ming Xiao. Design of air-sea integrated and coordinated air defense operation style. Flight Control and Detection, 2024, 7(2): 51−56
[70]	徐胜利, 张迪, 赵宏宇. 基于体系对抗的多弹协同制导技术研究. 战术导弹技术, 2019(1): 79−86 Xu Sheng-Li, Zhang Di, Zhao Hong-Yu. Research on the multi-missile cooperative technology based on systemic confrontation. Tactical Missile Technology, 2019(1): 79−86
[71]	孙景亮, 刘春生. 基于自适应动态规划的导弹制导律研究综述. 自动化学报, 2017, 43(7): 1101−1113 Sun Jing-Liang, Liu Chun-Sheng. An overview on the adaptive dynamic programming based missile guidance law. Acta Automatica Sinica, 2017, 43(7): 1101−1113
[72]	Ho Y, Bryson A, Baron S. Differential games and optimal pursuit-evasion strategies. IEEE Transactions on Automatic Control, 1965, 10(4): 385−389 doi: 10.1109/TAC.1965.1098197
[73]	花文华, 张拥军, 张金鹏, 孟庆龄. 双导弹拦截角度协同的微分对策制导律. 中国惯性技术学报, 2016, 24(6): 838−844 Hua Wen-Hua, Zhang Yong-Jun, Zhang Jin-Peng, Meng Qing-Ling. Differential game guidance law for double missiles with cooperative intercept angle. Journal of Chinese Inertial Technology, 2016, 24(6): 838−844
[74]	Bardhan R, Ghose D. Nonlinear differential games-based impact-angle-constrained guidance law. Journal of Guidance, Control, and Dynamics, 2015, 38(3): 384−402 doi: 10.2514/1.G000940
[75]	Taub I, Shima T. Intercept angle missile guidance under time varying acceleration bounds. Journal of Guidance, Control, and Dynamics, 2013, 36(3): 686−699 doi: 10.2514/1.59139
[76]	郭志强, 周绍磊. 多弹协同微分对策制导律研究. 兵器装备工程学报, 2019, 40(5): 21−25 Guo Zhi-Qiang, Zhou Shao-Lei. Research on cooperative differential game guidance law for multi-missile. Journal of Ordnance Equipment Engineering, 2019, 40(5): 21−25
[77]	Perelman T, Shima T, Rusnak T. Cooperative differential games strategies for active aircraft protection from a homing missile. Journal of Guidance, Control, and Dynamics, 2011, 34(3): 761−773 doi: 10.2514/1.51611
[78]	Shima T. Optimal cooperative pursuit and evasion strategies against a homing missile. Journal of Guidance, Control, and Dynamics, 2011, 34(2): 414−425 doi: 10.2514/1.51765
[79]	Rubinsky S, Gutman S. Three-player pursuit and evasion conflict. Journal of Guidance, Control, and Dynamics, 2014, 37(1): 98−110 doi: 10.2514/1.61832
[80]	Liu F, Dong X W, Li Q D, Ren Z. Cooperative differential games guidance laws for multiple attackers against an active defense target. Chinese Journal of Aeronautics, 2022, 35(5): 374−389 doi: 10.1016/j.cja.2021.07.033
[81]	Guo M C, de Persis C. Linear quadratic network games with dynamic players: Stabilization and output convergence to Nash equilibrium. Automatica, 2021, 130: Article No. 109711 doi: 10.1016/j.automatica.2021.109711
[82]	刘飞, 董希旺, 化永朝, 于江龙, 任章. 基于多联盟非合作博弈纳什均衡搜索的集群对抗方法. 指挥与控制学报, 2023, 9(6): 673−682 doi: 10.3969/j.issn.2096-0204.2023.06.0673 Liu Fei, Dong Xi-Wang, Hua Yong-Zhao, Yu Jiang-Long, Ren Zhang. Swarm confrontation method based on Nash equilibrium seeking in multi coalition non-cooperative games. Journal of Command and Control, 2023, 9(6): 673−682 doi: 10.3969/j.issn.2096-0204.2023.06.0673
[83]	王鑫, 闫杰, 孟廷伟. 高速目标分阶段博弈拦截制导策略. 航空学报, 2022, 43(9): Article No. 325598 doi: 10.7527/j.issn.1000-6893.2022.9.hkxb202209038 Wang Xin, Yan Jie, Meng Ting-Wei. High-speed target multi-stage interception scheme based on game theory. Acta Aeronautica et Astronautica Sinica, 2022, 43(9): Article No. 325598 doi: 10.7527/j.issn.1000-6893.2022.9.hkxb202209038
[84]	肖增博, 雷虎民, 滕江川, 张旭, 陈治湘. 目标飞行器反拦截协同制导策略. 兵工学报, 2011, 32(12): 1486−1492 Xiao Zeng-Bo, Lei Hu-Min, Teng Jiang-Chuan, Zhang Xu, Chen Zhi-Xiang. Cooperative guidance strategy in anti-interception for target aircrafts. Acta Armamentarii, 2011, 32(12): 1486−1492
[85]	陈洁卿, 孙瑞胜, 陈伟. 超声速导弹群协同博弈突防制导研究. 无人系统技术, 2021, 4(6): 65−74 Chen Jie-Qing, Sun Rui-Sheng, Chen Wei. Research on cooperative penetration game guidance of supersonic missile group. Unmanned Systems Technology, 2021, 4(6): 65−74
[86]	陈仔荣. 无人机避障突防与协同搜索一体化规划方法研究 [硕士学位论文], 国防科技大学, 中国, 2017. Chen Zi-Rong. Research on Integrated Route Planning Method of UAV Obstacle-avoidance Penetration and Cooperative Search [Master thesis], National University of Defense Technology, China, 2017.
[87]	李守义, 陈谋, 王玉惠, 吴庆宪, 贺建良. 非完备策略集下人机对抗空战决策方法. 中国科学: 信息科学, 2022, 52(12): 2239−2253 doi: 10.1360/SSI-2022-0222 Li Shou-Yi, Chen Mou, Wang Yu-Hui, Wu Qing-Xian, He Jian-Liang. Human-computer gaming decision-making method in air combat under an incomplete strategy set. Scientia Sinica Informationis, 2022, 52(12): 2239−2253 doi: 10.1360/SSI-2022-0222
[88]	倪炜霖, 王永海, 徐聪, 赤丰华, 梁海朝. 基于强化学习的高超飞行器协同博弈制导方法. 航空学报, 2023, 44(S2): Article No. 729400 Ni Wei-Lin, Wang Yong-Hai, Xu Cong, Chi Feng-Hua, Liang Hai-Zhao. Cooperative game guidance method for hypersonic vehicles based on reinforcement learning. Acta Aeronautica et Astronautica Sinica, 2023, 44(S2): Article No. 729400
[89]	郭明坤, 杨峰, 刘凯, 夏广庆, 杨竞楠. 高超声速飞行器协同制导技术研究进展. 空天技术, 2022(2): 75−84 Guo Ming-Kun, Yang Feng, Liu Kai, Xia Guang-Qing, Yang Jing-Nan. Review on cooperative guidance technology for hypersonic flight vehicle. Aerospace Technology, 2022(2): 75−84
[90]	王祥科, 刘志宏, 丛一睿, 李杰, 陈浩. 小型固定翼无人机集群综述和未来发展. 航空学报, 2020, 41(4): Article No. 023732 Wang Xiang-Ke, Liu Zhi-Hong, Cong Yi-Rui, Li Jie, Chen Hao. Miniature fixed-wing UAV swarms: Review and outlook. Acta Aeronautica et Astronautica Sinica, 2020, 41(4): Article No. 023732
[91]	王越, 赵凯, 刘学超, 杨维, 姚桐. 多防空武器平台一体化协同作战样式与关键技术探讨. 火炮发射与控制学报, 2022, 43(3): 91−95 Wang Yue, Zhao Kai, Liu Xue-Chao, Yang Wei, Yao Tong. Combat modes and key technologies of a multi air defense weapon platform in integrated cooperative operations. Journal of Gun Launch and Control, 2022, 43(3): 91−95
[92]	肖冰松, 方洋旺, 许蕴山, 曾宪伟, 胡诗国. 航空武器系统协同作战样式及关键技术. 火力与指挥控制, 2010, 35(4): 5−8 Xiao Bing-Song, Fang Yang-Wang, Xu Yun-Shan, Zeng Xian-Wei, Hu Shi-Guo. Modes and critical technologies in cooperative engagement for aviation weapon system. Fire Control and Command Control, 2010, 35(4): 5−8
[93]	张婷, 帅欢, 闫妍, 朱豪坤, 刘闯. 制导炸弹智能技术现状与发展思考. 导航与控制, 2022, 21(2): 21−29 doi: 10.3969/j.issn.1674-5558.2022.02.003 Zhang Ting, Shuai Huan, Yan Yan, Zhu Hao-Kun, Liu Chuang. Present situation and development of intelligent technology for guided bomb. Navigation and Control, 2022, 21(2): 21−29 doi: 10.3969/j.issn.1674-5558.2022.02.003
[94]	贾广新, 张品, 王永伟, 许静. 空面精确制导分布式智能协同的研究分析. 飞航导弹, 2021(5): 85−89 Jia Guang-Xin, Zhang Pin, Wang Yong-Wei, Xu Jing. Research and analysis of distributed intelligent collaboration for air surface precision guidance. Aerodynamic Missile Journal, 2021(5): 85−89