高超变体飞行器内点约束最小值原理突防制导

doi:10.12305/j.issn.1001-506X.2026.08.27

Abstract

Abstract:

When a hypersonic gliding vehicle with a variable-sweep wing attacks a target, considering the possibility of interception by a defense missile during the terminal guidance phase, a guidance method based on the minimum value principle with interior point constraints and a variable-shape switching strategy based on event-triggered mechanisms are designed. A penetration model under half-speed conditions is established. The miss distance of the defense missile is treated as an interior point constraint during the attack missile’s flight process. And the optimal acceleration is analyzed and solved using the minimum value principle. Using the event-triggered principle, the optimal vehicle shape, required attack angle, and sideslip angle corresponding to the control quantities of the optimization algorithm are solved. Simulation results show that the guidance method can help the variant vehicle evade interception by the defense missile, and the switcher can achieve the optimal shape switch that enhances the landing speed, demonstrating the effectiveness of the algorithm, which is further verified for robustness through Monte Carlo simulations.

Key words: hypersonic morphing vehicle, defense missile, minimum principle, interior point constraint, event triggering principle

CLC Number:

TJ 765.3

Dongdong YAO, Jianghua ZHOU, Qunli XIA, Jiawen XIE. Minimum principle penetration guidance for hypersonic morphing vehicle with interior point constraints[J]. Systems Engineering and Electronics, 2026, 48(8): 2821-2832.

Figures/Tables 22

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Table 1

References 32

1	任春艳, 刘颖, 张迁, 等. 2022年国外高超声速空面导弹发展动态研究[J]. 航空兵器, 2023, 30 (6): 18- 26.
	REN C Y, LIU Y, ZHANG Q, et al. Research on fortign air-to-ground hypersonic missile development in 2022[J]. Aero Weaponry, 2023, 30 (6): 18- 26.
2	武嘉明, 王俊伟, 李向阳. 美空射高超声速武器发展分析[J]. 战术导弹技术, 2024 (4): 123- 128.
	WU J M, WANG J W, LI X Y. Analysis on the development of U. S. air-launched hypersonic weapons[J]. Tactical Missile Technology, 2024 (4): 123- 128.
3	BRIAN G, ROBERTO F. Terminal adaptive guidance for autonomous hypersonic strike weapons via reinforcement Metalearning[J]. Journal of Spacecraft and Rockets, 2023, 60 (1): 13.
4	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.
	ZHAO L B, ZHU G S, ZHANG Y, et al. Key technologies and development trends of intelligent aircraft pursuit and escape game[J]. Aeronautical Missile, 2021 (12): 134- 139.
5	刘冰雁, 叶雄兵, 岳智宏, 等. 基于多组并行深度Q网络的连续空间追逃博弈算法[J]. 兵工学报, 2021, 42 (3): 663- 672. doi: 10.3969/j.issn.1000-1093.2021.03.024
	LIU B Y, YE X B, YUE Z L, et al. Continuous space pursuit-evasion game algorithm based on multi-group deep q network[J]. Acta Armamentarii, 2021, 42 (3): 663- 672. doi: 10.3969/j.issn.1000-1093.2021.03.024
6	JACOB T E, JAY P W. Defender-aware attacking guidance policy for the target-attacker-defender differential game[J]. Journal of Aerospace Information Systems, 2021, 18 (6): 322- 390.
7	倪炜霖, 王永海, 徐聪, 等. 基于强化学习的高超飞行器协同博弈制导方法[J]. 航空学报, 2023, 44 (S2): 729400.
	NI W L, WANG Y H, XU C, et al. Hypersonic vehicle cooperative game guidance method based on reinforcement learning[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44 (S2): 729400.
8	郭行. 高超声速飞行器博弈突防策略研究[D]. 西安: 西北工业大学, 2018.
	GUO X. Penetration game strategy for hypersonic vehicles[D]. Xi’an: Northwestern Polytechnical University. 2018.
9	王子瑶, 唐胜景, 郭杰, 等. 高超声速攻防博弈自适应微分对策三维制导[J]. 兵工学报, 2023, 44 (8): 2342- 2353.
	WANG Z Y, TANG S J, GUO J, et al. Adaptive 3-dimensional differential game guidance for hypersonic attack and defense[J]. Acta Armamentarii, 2023, 44 (8): 2342- 2353.
10	ADI M, VITALY S. Linear quadratic differential games guidance law with an intercept angle constraint and varying speed adversaries[J]. Journal of Guidance, Control, and Dynamics, 2022, 45 (11): 1980- 2201. doi: 10.2514/6.2023-2495
11	VITALY S. Optimal cooperative guidance laws in a multiagent target-missile-defender engagement[J]. Journal of Guidance, Control, and Dynamics, 2019, 42 (9): 1899- 2142.
12	VLADIMIR T, TAL S. Target evasion from a missile performing multiple switches in guidance law[J]. Journal of Guidance, Control, and Dynamics, 2016, 39 (10): 2205- 2468. doi: 10.2514/1.g000461
13	MARTIN W, TAL S. Minimum effort pursuit/evasion guidance with specified miss distance[J]. Journal of Guidance, Control, and Dynamics, 2016, 39 (5): 985- 1172.
14	VLADIMIR T, MARTIN W, TAL S. A combined linear–quadratic/bounded control differential game guidance law[J]. IEEE Trans. on Aerospace and Electronic Systems, 2021, 57 (5): 3452- 3462.
15	MEIR H, AMIRAM M, DAVID A. Rationalizable strategies for the navigator-target-missile game[J]. Journal of Guidance, Control, and Dynamics, 2020, 43 (6): 1039- 1224.
16	SASWAT P N, ADITYA P R, MANGAL K. Inverse geometric guidance strategy for a three-body differential game[C]//Proc. of the AIAA Scitech 2021 Forum, 2021.
17	AUSTIN A P, JESSE R M, ROBERT E R. Mach 5–3.5 morphing wave-rider accuracy and aerodynamic performance evaluation[J]. Journal of Aircraft, 2019, 56 (5): 2047- 2061.
18	CHEN H L, WANG P, TANG G J. Fuzzy disturbance observer-based fixed-time sliding mode control for hypersonic morphing vehicles with uncertainties[J]. IEEE Trans. on Aerospace and Electronic Systems, 2023, 59 (4): 3521- 3530.
19	YAO Z, WU S T. Intermittent gliding flight control design and verification of a morphing unmanned aerial vehicle[J]. IEEE Access, 2021, 7, 40991- 41005.
20	吴世超. 全速域乘波飞行器变体气动布局设计技术研究[D]. 长沙: 国防科技大学, 2021.
	WU S C. Aerodynamic layout design on deformation of waverider in full speed domain[D]. Changsha: National University of Defense Technology, 2021.
21	WEI C Z, JU X Z, HE F Y, et al. Research on non-stationary control of advanced hypersonic morphing vehicles[C]//Proc. of the 21st AIAA International Space Planes and Hypersonics Technologies Conference, 2017.
22	DAI P, YAN B B, LIU R F, et al. Integrated morphing strategy and trajectory optimization of a morphing waverider and its online implementation based on the neural network[J]. IEEE Access, 2021, 9, 59383- 59393. doi: 10.1109/ACCESS.2021.3073207
23	YAO D D, XIA Q L. Predictor–corrector guidance for a hypersonic morphing vehicle[J]. Aerospace, 2023, 10 (9): 795. doi: 10.3390/aerospace10090795
24	万泱泱, 郭杰, 王浩凝, 等. 落角约束下的高超声速变体飞行器末制导方法[J]. 飞行力学, 2024, 42 (1): 24- 31.
	WAN Y Y, GUO J, WANG H N, et al. Terminal guidance with impact angle constraints for hypersonic morphing vehicle[J]. Flight Dynamics, 2024, 42 (1): 24- 31.
25	张远, 黄万伟, 聂莹, 等. 一种高速可变形飞行器智能变形决策方法[J]. 宇航学报, 2022, 43 (12): 1665- 1675. doi: 10.3873/j.issn.1000-1328.2022.12.008
	ZHANG Y, HUANG W W, NIE Y, et al. An intelligent deformation decision making method for high speed morphing flight vehicle[J]. Journal of Astronautics, 2022, 43 (12): 1665- 1675. doi: 10.3873/j.issn.1000-1328.2022.12.008
26	王仰杰, 龙腾, 李俊志, 等. 高超变体飞行器再入轨迹罚函数序列凸规划[J]. 北京航空航天大学学报, 2025, 51 (5): 1747- 1759.
	WANG Y J, LONG T, LI J Z, et al. Reentry trajectory planning for hypersonic morphing vehicles using penalty sequence convex programming[J]. Journal of Beijing University of Aeronautics and Astronautics, 2025, 51 (5): 1747- 1759.
27	PING L. Entry guidance: a unified method[J]. Journal of Guidance, Control, and Dynamics, 2014, 37 (3): 713- 728.
28	DAI P, YAN B B, HUANG W, et al. Design and aerodynamic performance analysis of a variable-sweep-wing morphing waverider[J]. Aerospace Science and Technology, 2020, 98, 105703. doi: 10.1016/j.ast.2020.105703
29	钟宜生. 最优控制[M]. 北京: 清华大学出版社, 2015.
	ZHONG Y S. Optimal control[M]. Beijing: Tsinghua University Press, 2015.
30	SINHA A, KUMAR S R. Three-dimensional nonlinear cooperative salvo using event-triggered strategy[J]. Journal of Guidance, Control, and Dynamics, 2020, 44 (2): 328- 342. doi: 10.2514/1.g005367
31	WANG N Y, WANG X G, BIN E , et al. Three-dimensional adaptive dynamic surface guidance law for missile with terminal angle and field-of-view constraints[J]. ISA Transactions, 2024, 154, 113- 131.
32	ZHENG Z W, LI J Z, FEHAN M. Three-dimensional terminal angle constraint guidance law with class function-based adaptive sliding mode control[J]. Aerospace Science and Technology, 2024, 147, 109005. doi: 10.1016/j.ast.2024.109005

参数	Case1	Case2	Case3
效率/s	0.734	0.504	0.407
拦截规避	是	否	否
飞行时间/s	111.3	109	111.6
落角/（°）	−13	−20	−8.7
落速/（m/s）	1460	1405	1270

[1]	Yiheng LI, Qunli XIA, Mingkai WANG. Prescribed performance control of hypersonic morphing vehicle based on high-order fixed-time observer [J]. Systems Engineering and Electronics, 2025, 47(5): 1627-1637.
[2]	Shuaihao YAN, Mingying WEI, Yongbin ZHENG. Attitude control method of air defense missile based on large command change rate [J]. Systems Engineering and Electronics, 2024, 46(7): 2465-2474.
[3]	Yueqiang ZHAO, Shi AN, Qiang MAI, Qingyan XU, Yanan GUO. Effectiveness modeling of air defense missile weapon system based on ADC method [J]. Systems Engineering and Electronics, 2020, 42(9): 2003-2012.
[4]	Qingguo LIU, Xinxue LIU, Jian WU, Yaxiong LI. Optimization design for the parking orbit of a single space-to-ground vehicle [J]. Systems Engineering and Electronics, 2020, 42(1): 157-165.
[5]	DUAN Xiusheng, XU Gongguo, SHAN Ganlin. Solution to sensortarget assignment problem based on cooperative#br# memetic adaptive QPSO algorithm [J]. Systems Engineering and Electronics, 2016, 38(12): 2769-2776.
[6]	ZHAO Yueqiang1,2, MAI Qiang1, XU Qingyan3. Dependability modeling research of airdefense missile weapon systems [J]. Systems Engineering and Electronics, 2016, 38(12): 2777-2784.
[7]	ZHANG Da-yuan，LEI Hu-min，WU Ling，SHAO Lei，LI Jiong. A trajectory tracking guidance law based on sliding mode  variable structure control [J]. Systems Engineering and Electronics, 2014, 36(4): 721-727.
[8]	TANG Su-yan, MEI Shan, ZHU Yi-fan, LEI Yong-lin, LI Qun. Distributed weapon target assignment algorithm based on extended contract net protocol [J]. Journal of Systems Engineering and Electronics, 2011, 33(3): 568-574.
[9]	ZHU Yi-fan, TANG Su-yan, YU Wen-guang, LI Qun, LEI Yong-lin. Conditional contract net protocol based distributed guide-weapon assignment algorithm [J]. Journal of Systems Engineering and Electronics, 2011, 33(12): 2672-2678.
[10]	CHEN Li-xin. Concept of virtual server and its application in evaluation of fire efficiency with great intercepting depth [J]. Journal of Systems Engineering and Electronics, 2011, 33(10): 2230-2233.
[11]	TANG Su-yan, YU Wen-guang, ZHU Yi-fan, LI Zhi-ping, QING Du-zheng. Agent-based simulation and analysis of networking air defense missile systems [J]. Journal of Systems Engineering and Electronics, 2010, 32(12): 2632-2637.
[12]	ZHANG Wu1, ZHAO Zong-gui2, ZHAO Feng1, LIU Min1. Analysis of influencing factors on the optimal observer trajectory in bearings-only tracking [J]. Journal of Systems Engineering and Electronics, 2010, 32(1): 67-71.
[13]	ZHANG Su, CHENG Qi-yue, WANG Ying-long. Coordination efficiency evaluating of air-defense missile composite group [J]. Journal of Systems Engineering and Electronics, 2009, 31(8): 1923-1926.

Minimum principle penetration guidance for hypersonic morphing vehicle with interior point constraints

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