有限时间收敛的自适应滑模协同末制导

doi:10.12305/j.issn.1001-506X.2025.03.28

摘要/Abstract

摘要：

针对多高超声速飞行器的协同末制导问题, 提出一种有限时间收敛的自适应滑模协同制导方法, 能够同时满足终端航迹倾角、航迹方位角及时间协同的要求。分别从俯冲和转弯平面设计有限时间收敛的滑模协同制导律, 并设计滑模面自适应参数添加到制导律中。针对运动目标, 对飞行器与目标间的相对航迹倾角进行系数补偿, 解决打击运动目标时为减小脱靶而牺牲打击角度的问题。仿真结果表明, 该协同末制导律可以使各高超声速飞行器同时满足航迹倾角约束、打击时间协同及各自的终端航迹方位角要求, 且对于初始状态和气动参数偏差具有鲁棒性。

关键词: 多高超声速飞行器, 自适应滑模, 有限时间收敛, 协同末制导

Abstract:

Aiming at the cooperative terminal guidance problem of hypersonic vehicles, a finite-time convergent adaptive sliding mode cooperative guidance method is proposed. This method simultaneously satisfies the requirements of terminal track inclination angle, track azimuth angle, and time coordination. Finite-time convergent sliding mode cooperative guidance laws are designed separately for the dive plane and turning plane, and adaptive parameters of the sliding mode surface are incorporated into the guidance laws. For moving targets, coefficient compensation is applied to the relative track inclination angle between the vehicle and the target to resolve the issue of sacrificing the strike angle to reduce miss distance when targeting moving objects. Simulation results indicate that the cooperative guidance law enables each hypersonic vehicle to simultaneously satisfy the requirements of flight path angle constraints, timing coordination, and their respective terminal track angle, exhibiting robustness against the deviation of initial states and aerodynamic parameters.

Key words: multiple hypersonic vehicles, adaptive sliding mode, finite-time convergence, cooperative terminal guidance

中图分类号:

V448.2

黄绍洧, 都延丽, 刘燕斌, 王跃萍, 刘武. 有限时间收敛的自适应滑模协同末制导[J]. 系统工程与电子技术, 2025, 47(3): 961-969.

Shaowei HUANG, Yanli DU, Yanbin LIU, Yueping WANG, Wu LIU. Adaptive sliding cooperative terminal guidance with finite-time convergence[J]. Systems Engineering and Electronics, 2025, 47(3): 961-969.

图/表 11

图1

图2

表1

图3

图4

表2

表3

表4

图5

图6

图7

参考文献 32

1	ZHUC H,XUG D,WEIC Z,et al.Impact-time-control guidance law for hypersonic missiles in terminal phase[J].IEEE Access,2020,8,44611-44621. doi: 10.1109/ACCESS.2020.2971619
2	LIUS X,YANB B,HUANGW,et al.Current status and prospects of terminal guidance laws for intercepting hypersonic vehicles in near space: a review[J].Journal of Zhejiang University-Science A(Applied Physics & Engineering),2023,24(5):387-404.
3	李宏宇,尹童,敦晓彪.临近空间高超声速武器发展概况与防御体系研究[J].现代防御技术,2022,50(6):1-10.
	LIH Y,YINT,DUNX B.Overview of hypersonic weapon development and defense system research in near space[J].Modern Defence Technology,2022,50(6):1-10.
4	周敏,王一鸣,郭建国,等.多弹协同末制导方法综述[J].航空兵器,2023,30(4):17-25.
	ZHOUM,WAMGY M,GUOJ G,et al.A survey of multi-missile cooperative terminal guidance[J].Aero Weaponry,2023,30(4):17-25.
5	CHENJ Q,SUNR S,LUY.Cooperative game penetration guidance for multiple hypersonic vehicles under safety critical framework[J].Chinese Journal of Aeronautics,2024,37(1):247-255. doi: 10.1016/j.cja.2023.08.023
6	WANGJ H,CHENGL,CAIY W,et al.Low-order diving integrated guidance and control for hypersonic vehicles[J].Aerospace Science and Technology,2019,91,96-109. doi: 10.1016/j.ast.2019.04.045
7	WANGJ H,LIUL H,WANGP,et al.Guidance and control system design for hypersonic vehicles in dive phase[J].Aerospace Science and Technology,2016,53,47-60. doi: 10.1016/j.ast.2016.03.010
8	谭诗利,雷虎民,王斌.高超声速目标拦截含攻击角约束的协同制导律[J].北京理工大学学报,2019,39(6):597-602.
	TANS L,LEIH M,WANGB.Cooperative guidance law for hypersonic targets with constrained impact angle[J].Transactions of Beijing Institute of Technology,2019,39(6):597-602.
9	ERERK S,TEKINR.Impact time and angle control based on constrained optimal solutions[J].Journal of Guidance, Control, and Dynamics,2016,39(10):2448-2454. doi: 10.2514/1.G000414
10	ZHANGY,TANGS J,GUOJ.Two-stage cooperative guidance strategy using a prescribed-time optimal consensus method[J].Aerospace Science and Technology,2020,100,105641. doi: 10.1016/j.ast.2019.105641
11	ZHANGS,GUOY,LIUZ G,et al.Finite-time cooperative guidance strategy for impact angle and time control[J].IEEE Trans.on Aerospace and Electronic Systems,2020,57(2):806-819.
12	YOUH,CHANGX L,ZHAOJ F,et al.Three-dimensional impact-angle-constrained coorpe-rative guidance strategy against maneuvering target[J].ISA Transactions,2023,138,262-280. doi: 10.1016/j.isatra.2023.02.030
13	WANGC Y,YUH S,DONGW,et al.Three-dimensional impact angle and time control guidance law based on two-stage strategy[J].IEEE Trans.on Aerospace and Electronic Systems,2022,58(6):5361-5372. doi: 10.1109/TAES.2022.3169124
14	WANGC Y,WANGW L,DONGW,et al.Multiple-stage spatial-temporal cooperative guidance without time-to-go estimation[J].Chinese Journal of Aeronautics,2024,37(9):399-416. doi: 10.1016/j.cja.2024.05.026
15	LIG F,WUY J,XUP Y.Fixed-time cooperative guidance law with input delay for simultaneous arrival[J].International Journal of Control,2021,94(6):1664-1673. doi: 10.1080/00207179.2019.1662947
16	HES M,LIND F,WANGJ.Continuous second-order sliding mode based impact angle guidance law[J].Aerospace Science and Technology,2015,41,199-208. doi: 10.1016/j.ast.2014.11.020
17	TAHKM J,SHIMS W,HONGS M,et al.Impact time control based on time-to-go prediction for sea-skimming antiship missiles[J].IEEE Trans.on Aerospace and Electronic Systems,2018,54(4):2043-2052. doi: 10.1109/TAES.2018.2803538
18	CHENX T,WANGJ Z.Optimal control based guidance law to control both impact time and impact angle[J].Aerospace Science and Technology,2019,84,454-463. doi: 10.1016/j.ast.2018.10.036
19	HUQ L,HANT,XINM.New impact time and angle guidance strategy via virtual target approach[J].Journal of Guidance, Control, and Dynamics,2018,41(8):1755-1765. doi: 10.2514/1.G003436
20	KIMH G,LEEJ Y,KIMH J,et al.Look-angle-shaping guidance law for impact angle and time control with field-of-view constraint[J].IEEE Trans.on Aerospace and Electronic Systems,2019,56(2):1602-1612.
21	KANGS,TEKINR,HOLZAPFELF.Generalized impact time and angle control via look-angle shaping[J].Journal of Guidance, Control, and Dynamics,2019,42(3):695-702. doi: 10.2514/1.G003765
22	程志强,李涛,庞云福,等.变速度条件下控制攻击时间和角度的协同制导律[J].控制与决策,2024,39(5):1537-1542.
	CHENGZ Q,LIT,PANGY F,et al.Cooperative guidance law for impact time and angle control with variable speed[J].Control and Decision,2024,39(5):1537-1542.
23	张春妍,宋建梅,侯博,等.带落角和时间约束的网络化导弹协同制导律[J].兵工学报,2016,37(3):431-438.
	ZHANGC Y,SONGJ M,HOUB,et al.Cooperative guidance law with impact angle and impact time constraints for networked missiles[J].Acta Armamentarii,2016,37(3):431-438.
24	UNDURTI A. Optimal trajectories for maneuvering reentry vehicles[D]. Cambridge: Massachusetts Institute of Technology, 2007.
25	赵汉元.飞行器再入动力学和制导[M].长沙:国防科技大学出版社,1997.
	ZHAOH Y.Reentry dynamics and guidance of aircraft[M].Changsha:National University of Defense Technology,1997.
26	赵子恒,包长春.具有落角约束的全局复合滑模制导律[J].控制工程,2023,30(2):339-344.
	ZHAOZ H,BAOC C.Global composite sliding mode guidance law with angle constraint[J].Control Engineering of China,2023,30(2):339-344.
27	LEEJ I,JEONL S,TAHKM J.Homing guidance law for cooperative attack of multiple missiles[J].Journal of Guidance, Control, and Dynamics,2010,33(1):275-280.
28	穆忠伟,吴剑,韩秀枫.考虑落角约束的制导炸弹有限时间控制制导律[J].导航定位与授时,2020,7(4):89-95.
	MUZ W,WUJ,HANX F.Finite time control guidance law for guided bombs considering impact angle constraints[J].Navigation Positioning and Timing,2020,7(4):89-95.
29	ZHANGG S,LIX L.Design and analysis of a new power reaching law for sliding mode control[J].Journal of Tianjin University (Science and Technology),2020,53(11):1112-1119.
30	SONGJ H,SONGS M,XUS L.Three-dimensional cooperative guidance law for multiple missiles with finite-time convergence[J].Aerospace Science and Technology,2017,67,193-205.
31	ZHAOJ B,YANGS X.Integrated cooperative guidance framework and cooperative guidance law for multi-missile[J].Chinese Journal of Aeronautics,2018,31(3):546-555.
32	刘聪,刘俊彤,聂文田,等.多高超声速飞行器双阶段协同俯冲制导律设计方法研究[J].战术导弹技术,2022(4):41-49.
	LIUC,LIUJ T,NIEW T,et al.Research on design method of dual- stage cooperative dive guidance law for multiple hypersonic vehicles[J].Tactical Missile Technology,2022(4):41-49.

飞行器	H₀/km	θ₀/(°)	ϕ₀/(°)	V₀/(m/s)	γ₀/(°)	ψ₀/(°)
1	39	0.3	0.1	2 400	1.5	50
2	40	0.2	0.2	2 450	1.0	20
3	41	0.1	0.3	2 500	0.5	30

参数	飞行器
参数	1	2	3
t_{MT, i}/s	61.61	60.89	61.80
Δe_i/m	0.16	2.56	2.38
ψ_{f, i}/(°)	20.01	70.00	89.61

参数	飞行器
参数	1	2	3
t_{MT, i}/s	60.48	61.06	61.46
Δe_i/m	1.58	2.65	3.20
Δ$ \hat{e}$_i/m	1.65	1.04	2.59
γ_{f, i}/(°)	-59.88	-60.59	-57.62
$ \hat{\gamma}$_{f, i}/(°)	-39.86	-40.01	-40.13
ψ_{f, i}/(°)	19.91	71.09	89.85

状态	偏差	状态	偏差
H₀/m	±500	γ₀/(°)	±1
θ₀/(°)	±0.01	ψ₀/(°)	±1
ϕ₀/(°)	±0.01	V₀/(m/s)	±15
C_L/%	±20	C_D/%	±20

[1]	罗世彬, 李晓栋, 王忠森, 徐骋. 并联式运载器上升段广义超螺旋有限时间控制[J]. 系统工程与电子技术, 2022, 44(5): 1626-1635.
[2]	李军, 廖宇新, 李珺. 三维自适应有限时间超螺旋滑模制导律[J]. 系统工程与电子技术, 2021, 43(3): 779-788.
[3]	毛柏源, 李君龙, 张锐. 考虑自动驾驶仪动态特性的多约束中制导律[J]. 系统工程与电子技术, 2019, 41(2): 382-388.
[4]	刘正华, 温暖, 祝令谱. 变体飞行器有限时间收敛LPV鲁棒控制[J]. 系统工程与电子技术, 2018, 40(6): 1325-1330.
[5]	吕寿坤, 周荻, 孟克子, 王子才. 视线角约束自适应滑模中制导律[J]. 系统工程与电子技术, 2018, 40(4): 855-859.
[6]	李炯, 张涛, 雷虎民, 叶继坤, 王华吉. 非奇异快速终端二阶滑模有限时间制导律[J]. 系统工程与电子技术, 2018, 40(4): 860-867.
[7]	王晓芳，郑艺裕，林海. 导弹协同作战四维制导与控制一体化设计方法[J]. 系统工程与电子技术, 2015, 37(4): 874-881.
[8]	李伟明, 孙瑞胜, 白宏阳, 刘鹏云. 变后掠翼航弹最优弹道自适应滑模跟踪控制[J]. 系统工程与电子技术, 2015, 37(2): 372-378.
[9]	李伟明, 白宏阳, 辛明瑞, 申景诗. 时敏制导炸弹离散自适应滑模BTT自动驾驶仪设计[J]. 系统工程与电子技术, 2015, 37(11): 2579-2585.
[10]	方洁, 邓玮, 姜长生, 文杰. 具有扇区非线性输入的混沌系统函数投影同步[J]. Journal of Systems Engineering and Electronics, 2012, 34(9): 1872-1877.
[11]	徐世许，马建敏. 不确定多变量线性系统的快速收敛滑模控制[J]. Journal of Systems Engineering and Electronics, 2011, 33(7): 1585-1589.
[12]	樊仲光1,3，梁家荣2，肖剑1. 不确定奇异系统的Terminal滑模控制[J]. Journal of Systems Engineering and Electronics, 2010, 32(1): 158-161.