Trajectory tracking near asteroids using relaxed Lyapunov-based model predictive control

doi:10.23919/JSEE.2026.000098

Journal of Systems Engineering and Electronics ›› 2026, Vol. 37 ›› Issue (2): 670-686.doi: 10.23919/JSEE.2026.000098

• CONTROL THEORY AND APPLICATION • Previous Articles

Trajectory tracking near asteroids using relaxed Lyapunov-based model predictive control

Zhitong YU(), Haibin SHANG(), Zichen ZHAO(), Xuefen ZHANG()

School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

Received:2025-03-10 Online:2026-04-18 Published:2026-04-30
Contact: Haibin SHANG E-mail:bityzt@163.com;shanghb@bit.edu.cn;BitZhaozc@foxmail.com;bitzxf2021@163.com
About author:
YU Zhitong was born in 1995. He received his B.E. degree from Beijing Institute of Technology in 2018. He is currently a Ph.D. candidate in Beijing Institute of Technology. His research interests include trajectory tracking control, orbit dynamics and low energy transfer in multi-body system, asteroid exploration and defense. E-mail: bityzt@163.com

SHANG Haibin was born in 1980. He received his Ph.D. degree from Harbin Institute of Technology, Harbin, in 2008. He is currently a professor at the School of Aerospace Engineering, Beijing Institute of Technology. His research interests include design and analysis of deep space exploration mission, spacecraft orbit design, optimization and analysis, orbit dynamics and low energy transfer in multi-body system, and orbit dynamics and control in gravitational field of small bodies. E-mail: shanghb@bit.edu.cn

ZHAO Zichen was born in 1997. He received his B.E. degree from Beijing Institute of Technology in 2019. He is currently a Ph.D. candidate in Beijing Institute of Technology. His research interests include convex optimization, trajectory and attitude planning for aerospace vehicle, autonomous planning, guidance and control, gravity wave detection task, and unmanned aerial vehicle obstacle-free path planning. E-mail: BitZhaozc@foxmail.com

ZHANG Xuefen was born in 1998. She received his B.E. degree from Beijing Institute of Technology in 2019. She is currently a Ph.D. candidate in Beijing Institute of Technology. Her research interests include orbit dynamics near small bodies, trajectory planning, and uncertainty propagation. E-mail: bitzxf2021@163.com
Supported by:
This work was supported by the National Natural Science Foundation of China (12472354), the National Key Research and Development Program of China (2020YFC2200902), and the Key Technology Research Project of TW-3 (TW3005).

Abstract

Abstract:

Lyapunov-based model predictive control (LMPC) is an effective approach for trajectory tracking because of its well-guaranteed and easy-to-implement stability. However, traditional LMPC utilizes pre-designed auxiliary controllers to estimate the domain of attraction (DOA) and construct stability constraints, which inevitably reduces its stable domain and degrades tracking performance. For this problem, this paper proposes a relaxed LMPC (RLMPC) which is designed independently of auxiliary controllers. The control Lyapunov function (CLF) is firstly introduced to decouple the DOA and auxiliary control, alleviating the conservatism in traditional LMPC. Subsequently, a multi-resolution sampling-based search algorithm is developed to estimate the DOA, where the state space is partitioned into hyper-rectangles. A verification condition is derived to extend the verification validity of sampling points to all states within hyper-rectangles, thereby reducing DOA estimation error. Based on the auxiliary-controller-independent DOA (ACI-DOA) and CLF, stability constraints are formulated to ensure stability for RLMPC, while relaxing the stable domain of RLMPC to the entire ACI-DOA. Furthermore, a convergence rate adaptive adjustment technology is developed to enhance the convergence rate while balancing it with control effort. Through numerical simulations involving asteroid orbiting missions, the proposed method is found to significantly expand the stable domain and improve tracking performance.

Key words: Lyapunov-based model predictive control (LMPC), trajectory tracking, auxiliary-controller-independent domain of attraction (DOA), sampling-based search algorithm, control Lyapunov function (CLF), asteroid orbiting mission

Zhitong YU, Haibin SHANG, Zichen ZHAO, Xuefen ZHANG. Trajectory tracking near asteroids using relaxed Lyapunov-based model predictive control[J]. Journal of Systems Engineering and Electronics, 2026, 37(2): 670-686.

Figures/Tables 14

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Maximum convergence rate	Convergence time/s	Improvement/%	Control effort/(m/s)	Improvement/%
${\sigma _{{\text{user}}}} = 1$	1886.07	−	1.60	−
${\sigma _{{\text{user}}}} = 5$	1586.69	15.87	1.55	3.13
${\sigma _{{\text{user}}}} = 10$	1317.25	30.16	1.49	6.88
${\sigma _{{\text{user}}}} = 15$	987.94	47.62	1.44	10.00
${\sigma _{{\text{user}}}} = 20$	718.50	61.90	1.43	10.63
${\sigma _{{\text{user}}}} = 30$	808.25	57.15	1.53	4.38
${\sigma _{{\text{user}}}} = 50$	834.01	55.78	1.71	−
${\sigma _{{\text{user}}}} = 100$	868.13	53.97	1.82	−

Results	Statistic	LMPC	RLMPC	Improvement/%
Position error/m	Maximum value	13.88	3.06	−
	Minimum value	1.84	0.58	−
	Mean value	7.38	1.65	77.64
Control effort/(m/s)	Maximum value	2.67	2.81	−
	Minimum value	2.29	2.46	−
	Mean value	2.40	2.63	−
Convergence time/s	Maximum value	1320.72	728.23	−
	Minimum value	1590.35	937.41	−
	Mean value	1453.25	849.66	41.53

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Trajectory tracking near asteroids using relaxed Lyapunov-based model predictive control

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