Group cooperative midcourse guidance law design considering time-to-go

doi:10.23919/JSEE.2025.000065

Journal of Systems Engineering and Electronics ›› 2025, Vol. 36 ›› Issue (3): 835-853.doi: 10.23919/JSEE.2025.000065

• CONTROL THEORY AND APPLICATION • Previous Articles

Group cooperative midcourse guidance law design considering time-to-go

Ruitao ZHANG¹^,²^,³(), Yangwang FANG¹^,²^,³^,⁴(), Zhan CHEN¹^,²^,³(), Hang GUO¹^,²^,³^,⁴^,*(), Wenxing FU¹^,²^,³^,⁴()

¹ Unmanned System Research Institute, Northwestern Polytechnical University, Xi’an 710072, China
² National Key Laboratory of Unmanned Aerial Vehicle Technology, Xi’an 710072, China
³ Integrated Research and Development Platform of Unmanned Aerial Vehicle Technology, Xi’an 710072, China
⁴ Research Center for Unmanned System Strategy Development, Northwestern Polytechnical University, Xi’an 710072, China

Received:2024-04-07 Online:2025-06-18 Published:2025-07-10
Contact: Hang GUO E-mail:1476793301@qq.com;ywfang@nwpu.edu.cn;chenzhan@mail.nwpu.edu.cn;jsguoh@nwpu.edu.cn;wenxingfu@nwpu.edu.cn
About author:
ZHANG Ruitao was born in 1996. He received his B.S. degree in weapons system science and technology from North University of China, Taiyuan, China, in 2019. He is currently pursuing his Ph.D. degree in intelligent unmanned systems science and technology with the Unmanned System Research Institute, Northwestern Polytechnical University, Xi’an, China. His research interests include interceptor guidance and control, cooperative guidance, and collaboration of multi-agent system. E-mail: 1476793301@qq.com

FANG Yangwang was born in 1966. He received his B.S. degree in applied mathematics from Huaibei Normal University, Anhui, China, in 1987, M.S. degree in mathematics from Shaanxi Normal University, Xi’an, China, in 1990, and Ph.D. degree in control science and engineering from Xi’an Jiaotong University, Xi’an, China, in 1998. He is a professor and a doctoral supervisor with the Unmanned System Research Institute, Northwestern Polytechnical University, Xi’an, China. His research interests include interceptor navigation, guidance and control, multi-sensor fusion, performance evaluation, and collaboration of multi-agent system. E-mail: ywfang@nwpu.edu.cn

CHEN Zhan was born in 1996. He received his B.S. degree in mechatronic engineering from Tianjin University of Science and Technology, Tianjin, China, in 2018. He is currently pursuing his Ph.D. degree in intelligent unmanned systems science and technology with the Unmanned System Research Institute, Northwestern Polytechnical University, Xi’an, China. His research interests include interceptor navigation, guidance and control, target tracking, multi-sensor fusion, and collaboration of multi-agent system. E-mail: chenzhan@mail.nwpu.edu.cn

GUO Hang was born in 1990. He received his B.S., M.S., and Ph.D. degrees in navigation, guidance, and control from Northwestern Polytechnical University, in 2011, 2014, and 2019, respectively. He is currently an associate research fellow in Northwestern Polytechnical University. His research interests include hypersonic vehicle flight dynamics, guidance, and control. E-mail: jsguoh@nwpu.edu.cn

FU Wenxing was born in 1974. He received his B.S., M.S., and Ph.D. degrees in aircraft design from Northwestern Polytechnical University, Xi’an, China, in 2004. He is a professor and a doctoral supervisor with the Unmanned System Research Institute, Northwestern Polytechnical University, Xi’an, China. His research interests include interceptor navigation, guidance and control, multi-sensor fusion, and aircraft design. E-mail: wenxingfu@nwpu.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (62003264).

Abstract

Abstract:

To solve the problem of providing the best initial situation for terminal guidance when multiple missiles intercept multiple targets, a group cooperative midcourse guidance law (GCMGL) considering time-to-go is proposed. Firstly, a three-dimensional (3D) guidance model is established and a cooperative trajectory shaping guidance law is given. Secondly, for estimating the unknown target maneuvering acceleration, an adaptive disturbance observer (ADO) is designed, combining finite-time theory with a radial basis function (RBF) neural network, and the convergence of the estimation error is proven using Lyapunov stability theory. Then, to ensure time-to-go cooperation among missiles within the same group and across different groups, the group consensus protocols of virtual collision point mean and the inter-group cooperative consensus protocol are designed respectively. Based on the group consensus protocols, the virtual collision point cooperative guidance law is given, and the finite-time convergence is proved by Lyapunov stability theory. Simultaneously, combined with trajectory shaping guidance law, virtual collision point cooperative guidance law and the inter-group cooperative consensus protocol, the design of GCMGL considering time-to-go is given. Finally, numerical simulation results show the effectiveness and the superiority of the proposed GCMGL.

Key words: cooperative midcourse guidance, virtual collision point, time-to-go, finite-time theory, group consensus protocol

Ruitao ZHANG, Yangwang FANG, Zhan CHEN, Hang GUO, Wenxing FU. Group cooperative midcourse guidance law design considering time-to-go[J]. Journal of Systems Engineering and Electronics, 2025, 36(3): 835-853.

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Missile	Initial position $\left( {{x_0},{y_0},{z_0}} \right)/{\mathrm{m}}$	Initial velocity $\left( {{V_{x0}},{V_{y0}},{V_{z0}}} \right)/\left({\mathrm{m/s}} \right)$
Missile 1	$\left( {2\;500,10\;000, - 1\;500} \right)$	$\left( {1\;050,100,60} \right)$
Missile 2	$\left( {4\;000,11\;000, - 2\;000} \right)$	$\left( {1\;050,60,70} \right)$
Missile 3	$\left( {6\;000,11\;000, - 3\;000} \right)$	$\left( {1\;050,60,70} \right)$
Missile 4	$\left( {5\;000,8\;000,2\;000} \right)$	$\left( {1\;000,40,55} \right)$
Missile 5	$\left( {2\;000,8\;000, - 500} \right)$	$\left( {1\;000,40,55} \right)$
Missile 6	$\left( {0,8\;500, - 1\;000} \right)$	$\left( {1\;050,30,55} \right)$

Target	Initial position $\left( {{x_{\text{T}0}},{y_{\text{T}0}},{z_{\text{T}0}}} \right)/{\mathrm{m}}$	Initial velocity $\left( {{V_{\text{T}x0}},{V_{\text{T}y0}},{V_{\text{T}z0}}} \right)/\left({\mathrm{m/s}}\right)$
Target 1	$\left( {85\;000,11\;000,0} \right)$	$\left( {280,0,0} \right)$
Target 2	$\left( {90\;000,10\;000,500} \right)$	$\left( {280,0,0} \right)$

[1]	Hao YANG, Shifeng ZHANG, Xibin BAI, Chengye YANG. Impact time control guidance for moving-target considering velocity variation and field-of-view constraint [J]. Journal of Systems Engineering and Electronics, 2025, 36(2): 552-568.
[2]	Jia HUANG, Sijiang CHANG, Shengfu CHEN. A hybrid proportional navigation based two-stage impact time control guidance law [J]. Journal of Systems Engineering and Electronics, 2022, 33(2): 461-473.
[3]	Xiaojian Zhang, Mingyong Liu, and Yang Li. Sliding mode control and Lyapunov based guidance law with impact time constraints#br# [J]. Journal of Systems Engineering and Electronics, 2017, 28(6): 1186-1192.

Group cooperative midcourse guidance law design considering time-to-go

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