Fixed-time cooperative interception guidance law with angle constraints for multiple flight vehicles

doi:10.23919/JSEE.2025.000036

Journal of Systems Engineering and Electronics ›› 2025, Vol. 36 ›› Issue (2): 569-579.doi: 10.23919/JSEE.2025.000036

• CONTROL THEORY AND APPLICATION • Previous Articles

Fixed-time cooperative interception guidance law with angle constraints for multiple flight vehicles

Enjiao ZHAO¹^,*(), Xue DING¹(), Ke ZHANG²(), Zengyu YUAN³()

¹ College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China
² Wuhan Digital Engineering Institute, Wuhan 430074, China
³ Unit 92763 of the PLA, Dalian 116041, China

Received:2024-05-08 Online:2025-04-18 Published:2025-05-20
Contact: Enjiao ZHAO E-mail:zhaoenjiao935@163.com;dingxue991218@163.com;zk961020@163.com;navalyu@163.com
About author:
ZHAO Enjiao was born in 1989. She received her B.S. and M.S. degrees from Harbin Engineering University, Harbin, China, in 2011 and 2013, respectively. She received her Ph.D. degree in control science and engineering from the School of Astronautics, Harbin Institute of Technology in 2018. She is currently an associate professor in Harbin Engineering University. Her current research interests include cluster unmanned system cooperative control and intelligent navigation. E-mail: zhaoenjiao935@163.com

DING Xue was born in 1999. She received her B.S. degree from East China University of Technology, Nanchang, China, in 2022. She is currently working toward her M.S. degree in control science and engineering in the School of Automation, Harbin Engineering University. Her current research interests include multi-agent system and formation control. E-mail: dingxue991218@163.com

ZHANG Ke was born in 1996. He received his M.E. degree from Harbin Engineering University, Harbin, China, in 2023. He is an engineer in Wuhan Digital Engineering Institute now. His research interests include multi-agent system, formation control, and detection guidance. E-mail: zk961020@163.com

YUAN Zengyu was born in 1981. He received his B.S. degree in vessel command from Naval Marine Academy, Guangzhou, China, in 2004. He is an engineer in Unit 92763 of the PLA. His research interests include multi-agent system, underwater navigation system, and formation control. E-mail: navalyu@163.com
Supported by:
This work was supported by the National Natural Science Foundation of China (61903099), the Natural Science Foundation of Heilongjiang Province (LH2020F025), the Project of Science and Technology Research Program of Chongqing Education Commission of China (KJZD-K20200470), the Postdoctoral Science Foundation of China (2021M690812), and the Postdoctoral Science Fund of Heilongjiang Province (LBH-Z21048).

Abstract

Abstract:

This paper presents a fixed-time cooperative guidance method with impact angle constraints for multiple flight vehicles (MFV) to address the challenges of intercepting large maneuvering targets with difficulty and low precision. A cooperative guidance model is proposed, transforming the cooperative interception problem into a consensus problem based on the remaining flight time of the flight vehicles. First, the impact angle constraint is converted into the line of sight (LOS) angle constraint, and a new fixed-time convergent non-singular terminal sliding surface is introduced, which resolves the singularity issue of the traditional sliding surfaces. With this approach, LOS angle rate and normal overloads can converge in fixed time, ensuring that the upper bound of the system convergence time is not affected by the initial value of the system. Furthermore, the maneuvering movement of the target is considered as a system disturbance, and an extended state observer is employed to estimate and compensate for it in the guidance law. Lastly, by applying consensus theory and distributed communication topology, the remaining flight time of each flight vehicle is synchronized to ensure that they intercept the target simultaneously with different impact angles. Simulation experiments are conducted to validate the effectiveness of the proposed cooperative interception and guidance method.

Key words: fixed-time control, communication topology, consensus theory, impact angle, cooperative guidance

Enjiao ZHAO, Xue DING, Ke ZHANG, Zengyu YUAN. Fixed-time cooperative interception guidance law with angle constraints for multiple flight vehicles[J]. Journal of Systems Engineering and Electronics, 2025, 36(2): 569-579.

Figures/Tables 13

Fig 1

Table 1

Fig 2

Table 2

Fig 3

Fig 4

Fig 5

Fig 6

Fig 7

Fig 8

Table 3

Fig 9

Fig 10

References 31

1	ZHANG S, GUO Y, LIU Z G, et al Finite-time cooperative guidance strategy for impact angle and time control. IEEE Trans. on Aerospace and Electronic Systems, 2021, 2 (57): 806- 819.
2	CHENG Z T, SU M, LIU L, et al. A coordination law for multiple air vehicles in distributed communication scenarios. Journal of Advanced Transportation, 2020, 2020: 1810962.
3	LI G F, WU Y J Adaptive cooperative guidance with seeker-less followers: a position coordination-based framework. ISA Transactions, 2023, 143, 168- 176. doi: 10.1016/j.isatra.2023.09.024
4	AO L, HU X X, YANG S H, et al. Adaptive terminal time and impact angle constraint cooperative guidance strategy for multiple vehicles. Drones, 2024, 8(4): 134.
5	SHI P F, YU J L, DONG X Y, et al Distributed adaptive cooperative guidance against maneuvering targets with time-varying terminal angle constraint and overload saturation. Journal of the Franklin Institute, 2023, 360 (16): 11507- 11528.
6	LIU J H, YANG J Y An event-triggered optimal cooperative guidance law for simultaneous attacks with impact angle constraints. Optimal Control Applications and Methods, 2022, 43 (5): 1343- 1357.
7	CHEN S, MA D Y, YAO Y H, et al. Cooperative polynomial guidance law with collision avoidance and flight path angle coordination. Aerospace Science and Technology, 2022, 130: 107809.
8	LIU S X, YAN B B, ZHANG T, et al Coverage-based cooperative guidance law for intercepting hypersonic vehicles with overload constraint. Aerospace Science and Technology, 2022, 126, 107651.
9	CUI L, ZHEN Z, YANG J Y Fixed time cooperative scheme design for missiles salvo attack. IEEE Trans. on Circuits and Systems II-Express Briefs, 2024, 71 (2): 672- 676.
10	ZHANG Z, DONG X W, YV J L, et al Distributed cooperative tracking and cooperative guidance against maneuvering aerial target. Aerospace Science and Technology, 2024, 144, 108827.
11	YU J L, SHI Z X, DONG X W, et al Impact time consensus cooperative guidance against the maneuvering target: theory and experiment. IEEE Trans. on Aerospace and Electronic Systems, 2023, 59 (4): 4590- 4603.
12	GONG M, ZHOU S T, ZHOU D Optimal sliding mode guidance law against maneuvering target with impact angle constraint. Journal of Aerospace Engineering, 2024, 238 (5): 513- 528.
13	CHEN Y D, WANG J N, SHAN J Y, et al Cooperative guidance for multiple powered missiles with constrained impact and bounded speed. Journal of Guidance, Control, and Dynamics, 2021, 44 (4): 825- 841.
14	DONG F, ZHANG X Y, HE K P, et al A new three-dimensional adaptive sliding mode guidance law for maneuvering target with actuator fault and terminal angle constraints. Aerospace Science and Technology, 2022, 131, 107974.
15	YOU H, ZHAO J F, LI P, et al Nonsingular fast terminal second-order sliding mode guidance law with impact angle constraints. Journal of Projectiles, Rockets, Missiles and Guidance, 2019, 39 (6): 155- 159.
16	ZHANG X Y, ZHANG P, ZHENG X, et al Terminal angle constraint sliding mode guidance law design based on fixed-time convergence. Air & Space Defense, 2020, 3 (3): 9- 15.
17	SUN X J, ZHOU R, WU J Distributed cooperative guidance and control for multiple missiles. Journal of Beijing University of Aeronautics and Astronautics, 2014, 40 (1): 120- 124.
18	WANG L, ZOU M, GUO W L, et al Adaptive discontinuous control for fixed-time consensus of nonlinear multi-agent systems. Electronics, 2022, 11 (21): 3545. doi: 10.3390/electronics11213545
19	GUTMAN S Impact-time vector guidance. Journal of Guidance Control & Dynamics, 2017, 40 (8): 2110- 2114.
20	ZHANG N, GAI W D, ZHONG M Y, et al A fast finite-time convergent guidance law with nonlinear disturbance observer for unmanned aerial vehicles collision avoidance. Aerospace Science & Technology, 2019, 86, 204- 214.
21	ZHANG H G, HAN J, LUO C M, et al Fault-tolerant control of a nonlinear system based on generalized fuzzy hyperbolic model and adaptive disturbance observer. IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2017, 47 (8): 2289- 2300. doi: 10.1109/TSMC.2017.2652499
22	GONZALEZ A, BALAGUER V, CARCIA P, et al Gain-scheduled predictive extended state observer for time-varying delays systems with mismatched disturbances. ISA transactions, 2018, 84, 206- 213.
23	ZHANG Y, TANG S J, GUO J Adaptive terminal angle constraint interception against maneuvering targets with fast fixed-time convergence. International Journal of Robust and Nonlinear Control, 2018, 28 (8): 2996- 3014. doi: 10.1002/rnc.4067
24	CUI L, JIN N, CHANG S P, et al Fixed-time ESO based fixed-time integral terminal sliding mode controller design for a missile. ISA Transactions, 2021, 125, 237- 251.
25	HONG H F, YU W W, WEN G H, et al Distributed robust fixed-time consensus for nonlinear and disturbed multiagent systems. IEEE Trans. on Systems, 2017, 47 (7): 1464- 1473.
26	POLYAKOV A Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans. on Automatic Control, 2012, 57 (8): 2106- 2110. doi: 10.1109/TAC.2011.2179869
27	MA K M, MA J Design and implementation of variable structure guidance law for maneuvering target interception. Journal of Astronautics, 2010, 31 (6): 1589- 1595.
28	YANG L, YANG J Y Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems. International Journal of Robust and Nonlinear Control, 2011, 21 (16): 1865- 1879. doi: 10.1002/rnc.1666
29	TIAN Y, CAI Y L, DENG Y F A fast nonsingular terminal sliding mode control method for nonlinear systems with fixed-time stability guarantees. Journal of Chinese Inertail Technology, 2020, 28 (5): 677- 685.
30	ZHANG P, LIU H T, LI X B, et al Fault tolerance of cooperative interception using multiple flight vehicles. Journal of the Franklin Institute, 2013, 350 (9): 2373- 2395. doi: 10.1016/j.jfranklin.2013.02.022
31	ZUO Z Y, TIAN B L, DEFOORT M, et al Fixed-time consensus tracking for multiagent systems with high-order integrator dynamics. IEEE Trans. on Automatic Control, 2018, 63 (2): 563- 570. doi: 10.1109/TAC.2017.2729502

Vehicle	X/m	Y/m	V/(m/s)	θ/(°)
Target	10000	10000	30	−150
Vehicle 1	0	200	240	30
Vehicle 2	0	0	240	30
Vehicle 3	0	−200	240	30

Parameter	Value
$ \delta $	0.01
$ {\alpha _1} $	60
$ {\alpha _2} $	0.8
$ {\beta _1} $	60
$ {\beta _2} $	0.8
$ {m_1} $	1.2
$ {m_2} $	0.6
$ {n_1} $	1.2
$ {n_2} $	0.6
$ k $	1.1
$ d $	0

Variable	This paper	Proportional guidance
Guidance time/s	52.80	53.82
Off target quantity/m	0.2449	1.2646

[1]	Jiahui ZHANG, Qiuqiu WEN. Closed-form guidance law for velocity maximization with impact angle constraint [J]. Journal of Systems Engineering and Electronics, 2024, 35(5): 1295-1303.
[2]	Mengjing GAO, Tian YAN, Bingjie HAN, Haoyu CHENG, Wenxing FU, Bo HAN. Cooperative guidance law based on super-twisting observer for target maneuvering [J]. Journal of Systems Engineering and Electronics, 2024, 35(5): 1304-1314.
[3]	Yuanhe LIU, Nianhao XIE, Kebo LI, Yan’gang LIANG. Missile guidance law design based on free-time convergent error dynamics [J]. Journal of Systems Engineering and Electronics, 2024, 35(5): 1315-1325.
[4]	Jianping ZHOU, Wenjie ZHANG, Hang ZHOU, Qiang LI, Qunli XIA. Design of integral sliding mode guidance law based on disturbance observer [J]. Journal of Systems Engineering and Electronics, 2024, 35(1): 186-194.
[5]	Hang GUO, Zheng WANG, Bin FU, Kang CHEN, Wenxing FU, Jie YAN. Impact angle constrained fuzzy adaptive fault tolerant IGC method for Ski-to-Turn missiles with unsteady aerodynamics and multiple disturbances [J]. Journal of Systems Engineering and Electronics, 2022, 33(5): 1210-1226.
[6]	Shang SHI, Guosheng ZHANG, Huifang MIN, Yinlong HU, Yonghui SUN. Exact uncertainty compensation of linear systems by continuous fixed-time output-feedback controller [J]. Journal of Systems Engineering and Electronics, 2022, 33(3): 706-715.
[7]	Shengnan FU, Guanqun ZHOU, Qunli XIA. A trajectory shaping guidance law with field-of-view angle constraint and terminal limits [J]. Journal of Systems Engineering and Electronics, 2022, 33(2): 426-437.
[8]	Wei LI, Qiuqiu WEN, Lei HE, Qunli XIA. Three-dimensional impact angle constrained distributed cooperative guidance law for anti-ship missiles [J]. Journal of Systems Engineering and Electronics, 2021, 32(2): 447-459.
[9]	Biao YANG, Wuxing JING, Changsheng GAO. Three-dimensional cooperative guidance law for multiple missiles with impact angle constraint [J]. Journal of Systems Engineering and Electronics, 2020, 31(6): 1286-1296.
[10]	Yandong LI, Ling ZHU, Yuan GUO. Observer-based multivariable fixed-time formation control of mobile robots [J]. Journal of Systems Engineering and Electronics, 2020, 31(2): 403-414.
[11]	Wenjie ZHANG, Shengnan FU, Wei LI, Qunli XIA. An impact angle constraint integral sliding mode guidance law for maneuvering targets interception [J]. Journal of Systems Engineering and Electronics, 2020, 31(1): 168-184.
[12]	Xiaojian ZHANG, Mingyong LIU, Yang LI, Feihu ZHANG. Impact angle control over composite guidance law based on feedback linearization and finite time control [J]. Journal of Systems Engineering and Electronics, 2018, 29(5): 1036-1045.
[13]	Ran LI, Qiuqiu WEN, Wangchun TAN, Yijie ZHANG. Adaptive weighting impact angle optimal guidance law considering seeker's FOV angle constraints [J]. Journal of Systems Engineering and Electronics, 2018, 29(1): 142-151.
[14]	Wei Pang, Xiaofang Xie, and Tao Sun. Improved bias proportional navigation with multiple constraints for guide ammunition#br# [J]. Journal of Systems Engineering and Electronics, 2017, 28(6): 1193-1202.
[15]	Qingchun Li, Wensheng Zhang, Gang Han, and Yuan Xie. Fuzzy sliding mode control guidance law with terminal impact angle and acceleration constraints [J]. Systems Engineering and Electronics, 2016, 27(3): 664-679.

Fixed-time cooperative interception guidance law with angle constraints for multiple flight vehicles

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

Share this article

Figures/Tables 13

References 31

Related Articles 15

Recommended Articles

Metrics

Comments