Two-to-one differential game via improved MOGWO

doi:10.23919/JSEE.2025.000009

Journal of Systems Engineering and Electronics ›› 2025, Vol. 36 ›› Issue (1): 233-255.doi: 10.23919/JSEE.2025.000009

• CONTROL THEORY AND APPLICATION • Previous Articles

Two-to-one differential game via improved MOGWO

Yu BAI¹(), Di ZHOU¹^,*(), Bolun ZHANG²(), Zhen HE¹(), Ping HE³()

¹ School of Astronautics, Harbin Institute of Technology, Harbin 150001, China
² Beijing Institute of Electronic System Engineering, Beijing 100854, China
³ College of Engineering, Huazhong Agricultural University, Wuhan 430070, China

Received:2023-11-22 Online:2025-02-18 Published:2025-03-18
Contact: Di ZHOU E-mail:1260787968@qq.com;zhoud@hit.edu.com;bolun1104@163.com;hezhen@hit.edu.cn;pinghecn@qq.com
About author:
BAI Yu was born in 1996. He received his M.S. degree in control engineering from Northeastern University in 2021. He is currently pursuing his Ph.D. degree in control science and engineering at Harbin Institute of Technology, China. His research interests include missile guidance and control, and multi-objective optimization. E-mail: 1260787968@qq.com

ZHOU Di was born in 1969. He received his B.E. degree and Ph.D. degree in automatic control from Harbin Institute of Technology, Harbin, China, in 1991 and 1996, respectively. He is now a professor in the School of Astronautics, Harbin Institute of Technology. His research interests include nonlinear control, nonlinear filtering, and missile guidance and control. E-mail: zhoud@hit.edu.com

ZHANG Bolun was born in 1994. He received his B.E. degree in automatic control from Harbin Institute of Technology, Weihai, China, in 2017. He is currently pursuing his Ph.D. degree in guidance, navigation, and control at Harbin Institute of Technology, Harbin, China. His research interests include nonlinear control, and missile guidance and control. E-mail: bolun1104@163.com

HE Zhen was born in 1972. She received her B.E. degree and Ph.D. degree from Department of Automatic Control, Harbin Engineering University in 1995 and 2000, respectively. She is now a professor at Harbin Institute of Technology. Her research interest is the singular H∞ control description system. E-mail: hezhen@hit.edu.cn

HE Ping was born in 1989. He received his B.S. degree in automation from Sichuan University of Science and Engineering, Zigong, China, in 2012, M.S. degree in control science and engineering from Northeastern University of China, Shenyang, China, in 2014, and Ph.D. degree in electromechanical engineering from the University of Macau, Macau, China, in 2017. He is currently a professor at Huazhong Agricultural University, Wuhan, China. His research interests include robots, artificial intelligence, control theory, and control engineering. E-mail: pinghecn@qq.com
Supported by:
This work was supported by the National Natural Science Foundation of China (NSFC61773142; NSFC62303136).

Abstract

Abstract:

When the maneuverability of a pursuer is not significantly higher than that of an evader, it will be difficult to intercept the evader with only one pursuer. Therefore, this article adopts a two-to-one differential game strategy, the game of kind is generally considered to be angle-optimized, which allows unlimited turns, but these practices do not take into account the effect of acceleration, which does not correspond to the actual situation, thus, based on the angle-optimized, the acceleration optimization and the acceleration upper bound constraint are added into the game for consideration. A two-to-one differential game problem is proposed in the three-dimensional space, and an improved multi-objective grey wolf optimization (IMOGWO) algorithm is proposed to solve the optimal game point of this problem. With the equations that describe the relative motions between the pursuers and the evader in the three-dimensional space, a multi-objective function with constraints is given as the performance index to design an optimal strategy for the differential game. Then the optimal game point is solved by using the IMOGWO algorithm. It is proved based on Markov chains that with the IMOGWO, the Pareto solution set is the solution of the differential game. Finally, it is verified through simulations that the pursuers can capture the escapee, and via comparative experiments, it is shown that the IMOGWO algorithm performs well in terms of running time and memory usage.

Key words: differential game, improved multi-objective grey wolf optimization (IMOGWO), cooperative pursuit, optimal game point

Yu BAI, Di ZHOU, Bolun ZHANG, Zhen HE, Ping HE. Two-to-one differential game via improved MOGWO[J]. Journal of Systems Engineering and Electronics, 2025, 36(1): 233-255.

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References 33

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Item	IMOGWO	MOGWO
Iteration equation	Equation (35)	$ {\boldsymbol{D}} = \left\| { {\boldsymbol{C}} \cdot {{ {\boldsymbol{X}} }_P}\left( t \right) - {\boldsymbol{X}} \left( t \right)} \right\| $
Step	Equation (36)	$ {\boldsymbol{X}} \left( {t + 1} \right) = {\boldsymbol{X}} \left( t \right) - {\boldsymbol{A}} \cdot {\boldsymbol{ D}} $
Non-dominated solution	Law of the jungle	Find the non-dominated solution
Add new solution	Maximin fitness function	Grid mechanism
If achieve full	No limit	Update the grids
Research objective	Cost function 1−4	Function 1−10
Number of objectives	4	2 or 3
Number of iteration	<1000	<3000
Step size	[0,10]	[0,1]
Iteration population	50	100

Item	JetNano	Raspberry Pi
CPU	ARM CORTEX-A57	ARM CORTEX-A72
Storage	16GB EMMC 5.1	16GB EMMC 5.1
Memory/GB	4	4
Network	Gigabit Ethernet	Gigabit Ethernet

Project	Data
CPU	E5-2696V4
Internal storage	128g
Disk size	1T
System	Win10

Item	Effect	IMOGWO	MOGWO	MOPSO	MOGA
Running time/s	Average	0.33	0.37	0.42	0.40
	Midian	0.32	0.43	0.46	0.45
	Worst	0.62	0.73	0.74	0.70
	Best	0.16	0.19	0.27	0.23
Memory usage/MB	Average	52.7	58.3	65.4	63,2
	Midian	54.8	59.3	64.7	60.5
	Worst	62.5	64.2	70.6	71.2
	Best	50.3	56.4	62.5	56.5
Mission distance/m	Average	0.64	0.73	0.86	0.76
	Midian	0.73	0.76	0.83	0.79
	Worst	0.98	0.95	0.99	0.94
	Best	0.49	0.52	0.66	0.50
Accuracy/%	Average	95	88	76	89

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Two-to-one differential game via improved MOGWO

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