Rapid optimal control law generation: an MoE based method

doi:10.23919/JSEE.2025.000013

Journal of Systems Engineering and Electronics ›› 2025, Vol. 36 ›› Issue (1): 280-291.doi: 10.23919/JSEE.2025.000013

• CONTROL THEORY AND APPLICATION • Previous Articles

Rapid optimal control law generation: an MoE based method

Tengfei ZHANG¹(), Hua SU¹(), Chunlin GONG¹^,*(), Sizhi YANG²(), Shaobo BAI³()

¹ Shaanxi Aerospace Flight Vehicle Design Key Laboratory, School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China
² Northwest Industries Group Company, Xi’an 710043, China
³ Northwest Institute of Mechanical and Electrical Engineering, Xianyang 712099, China

Received:2024-01-18 Online:2025-02-18 Published:2025-03-18
Contact: Chunlin GONG E-mail:zhangtengfei@mail.nwpu.edu.cn;su@nwpu.edu.cn;leonwood@nwpu.edu.cn;yangsz@163.com;mbaishaobo@163.com
About author:
ZHANG Tengfei was born in 1997. He received his B.S. degree from the Honors College, Northwestern Polytechnical University, Xi’an, China in 2019. He is pursuing his Ph.D. degree at the School of Astronautics, Northwestern Polytechnical University. His research interests include trajectory optimization, computational guidance, and optimal parameter estimation. E-mail: zhangtengfei@mail.nwpu.edu.cn

SU Hua was born in 1985. He received his B.S., M.S., and Ph.D. degrees from Northwestern Polytechnical University, Xi’an, China in 2008, 2010, and 2014, respectively. He is an assistant researcher at the School of Astronautics, Northwestern Polytechnical University. His research interests include multidisciplinary design optimization and design software for flight vehicles. E-mail: su@nwpu.edu.cn

GONG Chunlin was born in 1980. He received his B.S., M.S., and Ph.D. degrees from Northwestern Polytechnical University, Xi’an, China in 2001, 2004, and 2007, respectively. He is currently a professor at the School of Astronautics, Northwestern Polytechnical University. His research interests include system engineering of flight vehicles and multidisciplinary design optimization. E-mail: leonwood@nwpu.edu.cn

YANG Sizhi was born in 1981. He received his Ph.D. degree from the School of Astronautics, Northwestern Polytechnical University, Xi’an, China in 2020. He is now a senior engineer in Northwest Industries Group Company. His research interests include aircraft design, guidance, and control technology. E-mail: yangsz@163.com

BAI Shaobo was born in 1997. He received his B.S. and M.S. degrees from the School of Astronautics, Northwestern Polytechnical University, Xi’an, China in 2015 and 2019. His research interests include trajectory optimization, computational guidance. E-mail: mbaishaobo@163.com
Supported by:
This work was supported by the Defense Industrial Technology Development Program (JCKY2020204B016), and the National Natural Science Foundation of China (92471206).

Abstract

Abstract:

To better complete various missions, it is necessary to plan an optimal trajectory or provide the optimal control law for the multirole missile according to the actual situation, including launch conditions and target location. Since trajectory optimization struggles to meet real-time requirements, the emergence of data-based generation methods has become a significant focus in contemporary research. However, due to the large differences in the characteristics of the optimal control laws caused by the diversity of tasks, it is difficult to achieve good prediction results by modeling all data with one single model. Therefore, the modeling idea of the mixture of experts (MoE) is adopted. Firstly, the K-means clustering algorithm is used to partition the sample data set, and the corresponding neural network classification model is established as the gate switch of MoE. Then, the expert models, i.e., the mappings from the generation conditions to the optimal control law represented by the results of principal component analysis (PCA), are represented by Kriging models. Finally, multiple rounds of accuracy evaluation, sample supplementation, and model updating are conducted to improve the generation accuracy. The Monte Carlo simulation shows that the accuracy of the proposed model reaches 96% and the generation efficiency meets the real-time requirement.

Key words: optimal control, mixture of experts (MoE), K-means, Kriging model, neural network classification, principal component analysis (PCA)

Tengfei ZHANG, Hua SU, Chunlin GONG, Sizhi YANG, Shaobo BAI. Rapid optimal control law generation: an MoE based method[J]. Journal of Systems Engineering and Electronics, 2025, 36(1): 280-291.

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Parameter type	Parameter name	Value
Mass properties/kg	Launch mass	109.8
	Mass after boost	99.5
	Empty mass	72.8
Engine characteristics	Thrust of booster engine/kN	10.8−14.8
	Burn time of booster engine/s	1.6−2.1
	Thrust of main engine/N	360−485
	Burn time of main engine/s	108−143

Variable	Lower boundary	Upper boundary
$ {H_{\text{a}}} $/km	0	3.6
$ {T_{\text{e}}} $/℃	−40	50
${H_0}$/km	1	10
${V_0}$/(m·s⁻¹)	20	270
$R$	${R_{\text{n}}}\left( {{{\boldsymbol{x}}_{\text{e}}}} \right)$	${R_{\text{f}}}\left( {{{\boldsymbol{x}}_{\text{e}}}} \right)$

Sample number	MoE model/%	Single model/%
2000	40.8	20.5
3000	52.1	27.1
5000	68.5	30.2
7000	69.2	36.5
10000	69.5	37.1

Case	${H_{\text{a}}}$/m	${T_{\text{e}}}$/℃	${H_0}$/m	${V_0}$/(m·s⁻¹)	$R$/m
1	0	50	8735	271	14719
2	500	0	9791	33	21177
3	3000	−40	1969	227	28286

Accuracy rate/%	Sample number	Memory/MB	CPU time/s	Error (mean and standard deviation)
Accuracy rate/%	Sample number	Memory/MB	CPU time/s	${\varepsilon _t}$/s	${\varepsilon _x}$/m	${\varepsilon _v}$/(m·s⁻¹)	${\varepsilon _\alpha }$/(°)
96.3	18 626	3.5	Average 0.007, and all<0.03	0.405 (2.133)	−8.298 (20.847)	0.046 (0.038)	0.040 (0.001)

Rapid optimal control law generation: an MoE based method

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