Online midcourse guidance method for intercepting high-speed gliding target

doi:10.23919/JSEE.2025.000133

Journal of Systems Engineering and Electronics ›› 2025, Vol. 36 ›› Issue (5): 1374-1388.doi: 10.23919/JSEE.2025.000133

• CONTROL THEORY AND APPLICATION • Previous Articles

Online midcourse guidance method for intercepting high-speed gliding target

Jinlin ZHANG¹^,*(), Jiong LI²(), Jikun YE²(), Humin LEI²(), Wanli LI¹(), Yangchao HE¹()

¹ Graduate School, Air Force Engineering University, Xi’an 710051, China
² Air Defense and Antimissile School, Air Force Engineering University, Xi’an 710051, China

Received:2023-11-27 Online:2025-10-18 Published:2025-10-24
Contact: Jinlin ZHANG E-mail:jlzhangnet@163.com;gracefuloo1@126.com;jikunbo@sina.com;hmleinet@126.com;liwl170@163.com;heyangchao0913@163.com
About author:
ZHANG Jinlin was born in 1997. He received his M.S. degree in control science and engineering from Air Force Engineering University in 2022. He is now a doctor student in control science and engineering at the Graduate School, Air Force Engineering University, Xi’an, China. His research interests include terminal guidance law and its capture space, trajectory optimization, and correction and regeneration of midcourse guidance. E-mail: jlzhangnet@163.com

LI Jiong was born in 1979. He received his M.S and Ph.D. degrees in control science and engineering from Air Force Engineering University. He is now an associate professor and a supervisor for doctors at the Air Defense and Antimissile School, Air Force Engineering University, Xi’an, China. His research interests include the advanced guidance law design, hypersonic interception, and missile automatic controller design. E-mail: gracefuloo1@126.com

YE Jikun was born in 1984. He received his M.S. and Ph.D. degrees in control science and engineering from the Air Defense and Antimissile School, Air Force Engineering University, in 2007 and 2012, respectively. He is currently an associate professor with the Department of Missile Engineering, Air Defense and Antimissile School, Air Force Engineering University. His research interests include nonlinear guidance and control. E-mail: jikunbo@sina.com

LEI Humin was born in 1960. He received his M.S. and Ph.D. degrees in navigation, guidance and control from Northwestern Polytechnical University, in 1989 and 1999, respectively. He is a professor and a supervisor for doctors in the Air Defense and Antimissile School, Air Force Engineering University, Xi’an, China. His current research interests are advanced guidance law design, hypersonic vehicle controller design, and hypersonic interception strategy. E-mail: hmleinet@126.com

LI Wanli was born in 1997. He received his M.S. degree in control science and engineering from Air Force Engineering University in 2021. He is now a doctor student in control science and engineering at the Graduate School, Air Force Engineering University, Xi’an, China. His research interests focus on the mid-guided missile trajectory optimization, correction, and regeneration. E-mail: liwl170@163.com

HE Yangchao was born in 1999. He received his B.S. degree in control science and engineering from Air Force Engineering University in 2021. He is now a doctor student in control science and engineering at the Graduate School, Air Force Engineering University, Xi’an, China. His research interests include trajectory generation, and tracking and prediction algorithms of reentry gliding vehicle. E-mail: heyangchao0913@163.com

Abstract

Abstract:

In this paper, an online midcourse guidance method for intercepting high-speed maneuvering targets is proposed. Firstly, the affine system is used to build a dynamic model and analyze the state constraints. The midcourse guidance problem is transformed into a continuous time optimization problem. Secondly, the problem is transformed into a discrete convex programming problem by affine control variable relaxation, Gaussian pseudospectral discretization and constraints linearization. Then, the off-line midcourse guidance trajectory is generated before midcourse guidance. It is used as the initial reference trajectory for online correction of midcourse guidance. An online guidance framework is used to eliminate the error caused by calculation of guidance instruction time. And the design of discrete points decreases with flight time to improve the solving efficiency. In addition, it is proposed that the terminal guidance capture is used innovatively space to judge the success of midcourse guidance. Numerical simulation shows the feasibility and effectiveness of the proposed method.

Key words: convex programming, capture space, online midcourse guidance, interception

Jinlin ZHANG, Jiong LI, Jikun YE, Humin LEI, Wanli LI, Yangchao HE. Online midcourse guidance method for intercepting high-speed gliding target[J]. Journal of Systems Engineering and Electronics, 2025, 36(5): 1374-1388.

Figures/Tables 9

Fig 1

Fig 2

Fig 3

Table 1

Table 2

Fig 4

Fig 5

Fig 6

Fig 7

References 41

1	MALYYTA D, YU Y, ELANGO P, et al Advances in trajectory optimization for space vehicle control. Annual Reviews in Control, 2021, 52, 282- 315. doi: 10.1016/j.arcontrol.2021.04.013
2	LI M J, CHOU C J, LEI H M, et al An intelligent trajectory prediction algorithm of reentry gliding target based on control parameter estimation. Systems Engineering and Electronics, 2024, 45 (1): 221- 233.
3	LI Z, WANG Y D, ZHENG W Accurately tracking hypersonic gliding vehicles via an LEO mega-constellation in relay tracking mode. Journal of Systems Engineering and Electronics, 2024, 35 (1): 211- 221. doi: 10.23919/JSEE.2023.000078
4	ZHOU J P, ZHENG W J, ZHOU H, et al Design of integral sliding mode guidance law based on disturbance observer. Journal of Systems Engineering and Electronics, 2024, 35 (1): 186- 194. doi: 10.23919/JSEE.2023.000111
5	DING C W, ZHOU D, ZOU X G, et al Multiple model PHD filter for tracking sharply maneuvering targets using recursive RANSAC based adaptive birth estimation. Journal of Systems Engineering and Electronics, 2024, 35 (3): 780- 792. doi: 10.23919/JSEE.2023.000134
6	LIU S X, YAN B B, HUANG W, et al Current status and prospects of terminal guidance laws for intercepting hypersonic vehicles in near space: a review. Journal of Zhejiang University-SCIENCE A, 2023, 24 (5): 387- 403. doi: 10.1631/jzus.A2200423
7	LI W L, LI J, LEI H M Discussion on neighborhood optimal trajectory online correction algorithm and its application range. Journal of Systems Engineering and Electronics, 2023, 34 (4): 1053- 1062. doi: 10.23919/JSEE.2023.000097
8	WAN S Z, CHANG X F, LI Q C, et al Suboptimal midcourse guidance with terminal-angle constraint for hypersonic target interception. International Journal of Aerospace Engineering, 2019, 2019, 6161032.
9	SHIN H S, LI K B An improvement in three-dimensional pure proportional navigation guidance. IEEE Trans. on Aerospace and Electronic Systems, 2021, 57 (5): 3004- 3014. doi: 10.1109/TAES.2021.3067656
10	CALISE A J Adaptive finite time intercept guidance. Journal of Guidance, Control, and Dynamics, 2023, 46 (10): 1975- 1980. doi: 10.2514/1.G007664
11	LIU S X, YAN B B, ZHANG T, et al. Three-dimensional coverage-based cooperative guidance law with overload constraints to intercept a hypersonic vehicle. Aerospace Science and Technology, 2022, 130: 107908.
12	QI W, LIAO Z Z Computational intelligence interception guidance law using online off-policy integral reinforcement learning. Journal of Systems Engineering and Electronics, 2024, 35 (4): 1042- 1052. doi: 10.23919/JSEE.2024.000067
13	XI A, CAI Y L A nonlinear finite-time robust differential game guidance law. Sensors, 2022, 22 (17): 6650. doi: 10.3390/s22176650
14	LEI H M, ZHOU J, ZHAI D, et al Optimal midcourse trajectory cluster generation and trajectory modification for hypersonic interceptions. Journal of Systems Engineering and Electronics, 2017, 28 (6): 1162- 1173. doi: 10.21629/JSEE.2017.06.14
15	ZHOU J, LEI H M, SHAO L, et al Optimal midcourse trajectory planning considering the capture region. Journal of Systems Engineering and Electronics, 2018, 29 (3): 587- 600. doi: 10.21629/JSEE.2018.03.16
16	MONDAL S, PADHI R Angle-constrained terminal guidance using quasi-spectral model predictive static programming. Journal of Guidance, Control, and Dynamics, 2017, 41 (3): 779- 787.
17	ZHOU C, HE L, YAN X D, et al Active-set pseudospectral model predictive static programming for midcourse guidance. Aerospace Science and Technology, 2023, 134, 108137. doi: 10.1016/j.ast.2023.108137
18	ZHANG G X, PANG B, WEN C, et al Semi-analytical midcourse guidance for coordinated interception of multiple exo-atmospheric targets. Journal of Spacecraft and Rockets, 2024, 61 (1): 34- 47. doi: 10.2514/1.A35659
19	LI W L, LI J, LI N B, et al Online trajectory planning method for midcourse guidance phase based on deep reinforcement learning. Aerospace, 2023, 10 (5): 441. doi: 10.3390/aerospace10050441
20	CHEN W Y, LI W M, SHAO L, et al Correction strategy of online midcourse guidance for high-speed gliding target interceptor. Applied Sciences, 2023, 13 (11): 6661. doi: 10.3390/app13116661
21	NGUYEN N T, TRAN V N On the solution existence to convex polynomial programs and its applications. Optimization Letters, 2021, 15 (2): 719- 731. doi: 10.1007/s11590-020-01686-w
22	LIU X F, LU P, PAN B F Survey of convex optimization for aerospace applications. Astrodynamics, 2017, 1 (1): 23- 40. doi: 10.1007/s42064-017-0003-8
23	LIU X F, LU P Solving nonconvex optimal control problems by convex optimization. Journal of Guidance, Control, and Dynamics, 2014, 37 (3): 750- 765. doi: 10.2514/1.62110
24	LIU X F, SHEN Z J, LU P Entry trajectory optimization by second-order cone programming. Journal of Guidance, Control, and Dynamics, 2016, 39 (2): 227- 241. doi: 10.2514/1.G001210
25	LIU X F, SHEN Z J, LU P Exact convex relaxation for optimal flight of aerodynamically controlled missiles. IEEE Trans. on Aerospace and Electronic Systems, 2016, 52 (4): 1881- 1892. doi: 10.1109/TAES.2016.150741
26	LIU X F Fuel-optimal rocket landing with aerodynamic controls. Journal of Guidance, Control, and Dynamics, 2019, 42 (1): 65- 77. doi: 10.2514/1.G003537
27	SAGLIANO M Pseudospectral convex optimization for powered descent and landing. Journal of Guidance, Control, and Dynamics, 2018, 41 (2): 320- 334. doi: 10.2514/1.G002818
28	HAN H W, QIAO D, CHEN H B, et al Rapid planning for aerocapture trajectory via convex optimization. Aerospace Science and Technology, 2019, 84, 763- 775. doi: 10.1016/j.ast.2018.11.009
29	WANG J B, CUI N G, WEI C Z Rapid trajectory optimization for hypersonic entry using convex optimization and pseudospectral method. Aircraft Engineering and Aerospace Technology, 2019, 91 (4): 669- 679. doi: 10.1108/AEAT-06-2018-0159
30	KUMAGAI N, OGURI K Adaptive-mesh sequential convex programming for space trajectory optimization. Journal of Guidance, Control, and Dynamics, 2024, 47 (10): 2213- 2220. doi: 10.2514/1.G008107
31	YANG B, JING W X, GAO C S Online midcourse guidance method for boost phase interception via adaptive convex programming. Aerospace Science and Technology, 2021, 118, 107037. doi: 10.1016/j.ast.2021.107037
32	SAGLIANO M, ERWIN M Optimal drag-energy entry guidance via pseudospectral convex optimization. Aerospace Science and Technology, 2021, 117, 106946. doi: 10.1016/j.ast.2021.106946
33	ZHANG J L, LI J, ZHOU C J, et al. Fast trajectory generation method for midcourse guidance based on convex optimization. International Journal of Aerospace Engineering, 2022, 2022: 7188718.
34	ZHOU X, ZHANG H B, XIE L, et al An improved solution method via the pole-transformation process for the maximum- crossrange problem. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2020, 234 (9): 1491- 1506. doi: 10.1177/0954410020914809
35	ZHOU X, HE R Z, ZHANG H B, et al Sequential convex programming method using adaptive mesh refinement for entry trajectory planning problem. Aerospace Science and Technology, 2021, 109, 106374. doi: 10.1016/j.ast.2020.106374
36	LI M J, ZHOU C J, SHAO L, et al A trajectory generation algorithm for a re-entry gliding vehicle based on convex optimization in the flight range domain and distributed grid points adjustment. Applied Sciences, 2023, 13 (3): 1988. doi: 10.3390/app13031988
37	ZHANG J L, LI J, LEI H M, et al Capture region of 3D realistic true proportional navigation with finite overload. Systems Engineering and Electronics, 2022, 44 (3): 986- 997.
38	LI K B, BAI Z H, SHIN H S, et al Capturability of 3D RTPN guidance law against true-arbitrarily maneuvering target with maneuverability limitation. Chinese Journal of Aeronautics, 2022, 35 (7): 75- 90. doi: 10.1016/j.cja.2021.10.004
39	ZHANG J B, XIONG J J, LI L Z, et al Motion state recognition and trajectory prediction of hypersonic glide vehicle based on deep learning. IEEE Access, 2022, 10, 21095- 21108. doi: 10.1109/ACCESS.2022.3150830
40	LI F, XIONG J, LAN X H, et al Hypersonic vehicle trajectory prediction algorithm based on hough transform. Chinese Journal of Electronics, 2021, 30 (5): 918- 930. doi: 10.1049/cje.2021.07.003
41	DOMAHIDI A, CHU E, BOYD S. ECOS: an SOCP solver for embedded systems. Proc. of the European Control Conference, 2013: 3071−3076.

Parameter	Value
h₀/km	40
z₀/km	0
x₀/km	0
v₀/(km/s)	2.5
$ {\theta _0} $/(°)	5
$ {\psi _0} $/(°)	0
h_f/km	23
z_f/km	20
x_f/km	400
v_f/(km/s)	−
$ {\theta _f} $/(°)	0
$ {\psi _f} $/(°)	10

Method	Parameter	Value
GPOPS	Solution accuracy/m	0
	Iterations number	7
	Total solution time/s	7.818 1
Proposed	Solution accuracy/m	2.637 8
	Iterations number	3
	Total solution time/s	1.716 4

[1]	Yangjie LYU, Yan GAO, Guoyuan QI. Multicopter interception control based on visual servo and virtual tube in a cluttered environment [J]. Journal of Systems Engineering and Electronics, 2025, 36(4): 1094-1102.
[2]	Qi WANG, Zhizhong LIAO. Computational intelligence interception guidance law using online off-policy integral reinforcement learning [J]. Journal of Systems Engineering and Electronics, 2024, 35(4): 1042-1052.
[3]	Yi NAN, Guoxing YI, Lei HU, Changhong WANG, Zhenbiao TU. Influencing factor analysis of interception probability and classification-regression neural network based estimation [J]. Journal of Systems Engineering and Electronics, 2023, 34(4): 992-1006.
[4]	Wenyu CHEN, Lei SHAO, Humin LEI. On-line trajectory generation of midcourse cooperative guidance for multiple interceptors [J]. Journal of Systems Engineering and Electronics, 2022, 33(1): 197-209.
[5]	Xin ZENG, Yanwei ZHU, Leping YANG, Chengming ZHANG. A guidance method for coplanar orbital interception based on reinforcement learning [J]. Journal of Systems Engineering and Electronics, 2021, 32(4): 927-938.
[6]	Shanshan WANG, Zheng LIU, Rong XIE, Jingjing WANG. VCR-LFM-BPSK signal design for countering advanced interception technologies [J]. Journal of Systems Engineering and Electronics, 2021, 32(2): 380-388.
[7]	Jin ZHOU, Lei SHAO, Huaji WANG, Dayuan ZHANG, Humin LEI. Optimal midcourse trajectory planning considering the capture region [J]. Journal of Systems Engineering and Electronics, 2018, 29(3): 587-600.
[8]	Hu Dandan, Yang Chao & Yang Jun. Budget constrained flow interception location model for congested systems? [J]. Journal of Systems Engineering and Electronics, 2009, 20(6): 1255-1262.
[9]	Hu Dandan, Yang Chao & Yang Jun. Model and algorithm of flow interception problem with multi-type of flows [J]. Journal of Systems Engineering and Electronics, 2009, 20(4): 755-761.

Online midcourse guidance method for intercepting high-speed gliding target

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

Share this article

Figures/Tables 9

References 41

Related Articles 9

Recommended Articles

Metrics

Comments