Threat sequencing of multiple UCAVs with incomplete information based on game theory

doi:10.23919/JSEE.2022.000095

Journal of Systems Engineering and Electronics ›› 2022, Vol. 33 ›› Issue (4): 986-996.doi: 10.23919/JSEE.2022.000095

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Threat sequencing of multiple UCAVs with incomplete information based on game theory

Shouyi LI(), Mou CHEN*(), Qingxian WU(), Yuhui WANG()

¹ College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China

Received:2021-06-03 Accepted:2022-06-09 Online:2022-08-30 Published:2022-08-30
Contact: Mou CHEN E-mail:shouyili@163.com;chenmou@nuaa.edu.cn;wuqingxian@nuaa.edu.cn;wangyh@nuaa.edu.cn
About author:|LI Shouyi was born in 1991. He received his B.S. degree in mathematics and applied mathematics from Shandong Agricultural University, Taian, China, in 2014. He is currently pursuing his Ph.D. degree in control theory and control engineering, with Nanjing University of Aeronautics and Astronautics. His research interests include fire and command control, game theory, reinforcement learning, and their applications in autonomous decision-making system. E-mail: shouyili@163.com||CHEN Mou was born in 1975. He received his B.S. degree in material science and engineering and Ph.D. degree in control theory and control engineering from Nanjing University of Aeronautics and Astronautics (NUAA), in 1998 and 2004, respectively. He is currently a full professor with the College of Automation Engineering, NUAA. His current research interests include nonlinear system control, intelligent control, and flight control. E-mail: chenmou@nuaa.edu.cn||WU Qingxian was born in 1955. He obtained his M.S. degree in control theory and application from Southeast University, Nanjing, China, in 1985. Currently, he is a professor and Ph.D. supervisor at Nanjing University of Aeronautics and Astronautics. His main research fields are industrial automation, robust control, and intelligent control. E-mail: wuqingxian@nuaa.edu.cn||WANG Yuhui was born in 1980. She received her B.S. degree in electrical engineering and its automation from University of Ji’nan, Ji’nan, China, in 2001, and Ph.D. degree in control theory and control engineering from Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China, in 2008. She is currently a full professor with the College of Automation Engineering, NUAA. Her current research interests include nonlinear system control, intelligent control, and flight control. E-mail: wangyh@nuaa.edu.cn
Supported by:
This work was supported by the Major Projects for Science and Technology Innovation 2030 (2018AAA0100805)

Abstract

Abstract:

The threat sequencing of multiple unmanned combat air vehicles (UCAVs) is a multi-attribute decision-making (MADM) problem. In the threat sequencing process of multiple UCAVs, due to the strong confrontation and high dynamics of the air combat environment, the weight coefficients of the threat indicators are usually time-varying. Moreover, the air combat data is difficult to be obtained accurately. In this study, a threat sequencing method of multiple UCAVs is proposed based on game theory by considering the incomplete information. Firstly, a zero-sum game model of decision maker ( $\mathcal{D}$ ) and nature ( $\mathcal{N}$ ) with fuzzy payoffs is established to obtain the uncertain parameters which are the weight coefficient parameters of the threat indicators and the interval parameters of the threat matrix. Then, the established zero-sum game with fuzzy payoffs is transformed into a zero-sum game with crisp payoffs (matrix game) to solve. Moreover, a decision rule is addressed for the threat sequencing problem of multiple UCAVs based on the obtained uncertain parameters. Finally, numerical simulation results are presented to show the effectiveness of the proposed approach.

Key words: threat sequencing, multiple unmanned combat air vehicles (UCAVs), multi-attribute decision-making (MADM), game theory, incomplete information

Shouyi LI, Mou CHEN, Qingxian WU, Yuhui WANG. Threat sequencing of multiple UCAVs with incomplete information based on game theory[J]. Journal of Systems Engineering and Electronics, 2022, 33(4): 986-996.

Figures/Tables 4

Fig 1

Table 1

Fig 2

Fig 3

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Symbol	Description	${\boldsymbol{B}_1}$	${\boldsymbol{B}_2}$	${\boldsymbol{B}_3}$	${\boldsymbol{B}_4}$	${ {{\boldsymbol{R}}}_0}$
${p_{ix}}$ /km	$X$ coordinate of position	[?14,?12]	[21,23]	[?17,?15]	[17,19]	0
${p_{iy}}$ /km	$Y$ coordinate of position	[21,24]	[?17,?14]	[16,19]	[?15,?12]	0
${p_{iz}}$ /km	$Z$ coordinate of position	[12,14]	[21,23]	[?4,?3]	[22,24]	0
${v_{ix}}$ /(km·h^?1)	$X$ coordinate of speed	[35,37]	[?56,?52]	[83,87]	[53,58]	[91,97]
${v_{iy}}$ /(km·h^?1)	$Y$ coordinate of speed	[56,59]	[93 98]	[73,78]	[84,87]	[61,64]
${v_{iz}}$ /(km·h^?1)	$Z$ coordinate of speed	[53,56]	[71,73]	[84,88]	[94,97]	[37,40]
${m_i}$ /km	Missile attack distance	[30,33]	[31,34]	[29,31]	[26,28]	[42,44]
${r_i}$ /km	Radar detection distance	[81,87]	[82,89]	[90,94]	[84,87]	[91,98]
$\varepsilon _i^m$	Maneuverability performance	[1.3,1.5]	[1.5,1.6]	[2.4,2.6]	[1.4,1.6]	?
$\varepsilon _i^f$	Firepower performance	[0.4,0.5]	[0.7,0.9]	[0.6,0.7]	[0.5,0.6]	?
$\varepsilon _i^d$	Detection performance	[0.8,0.9]	[0.4,0.5]	[0.6,0.8]	[0.7,0.9]	?
$\varepsilon _i^h$	Handling performance	[0.6,0.7]	[0.5,0,6]	[0.3,0.4]	[0.4,0.5]	?
$\varepsilon _i^s$	Survival performance	[0.4,0.5]	[0.7,0.8]	[0.4,0.6]	[0.5,0.6]	?
$\varepsilon _i^v$	Voyage coefficient	[0.3,0.5]	[0.6,0.7]	[0.5,0.6]	[0.4,0.5]	?
$\varepsilon _i^e$	Electronic countermeasure performance	[0.3,0.4]	[0.5,0.6]	[0.7,0.9]	[0.4,0.5]	?

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Threat sequencing of multiple UCAVs with incomplete information based on game theory

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