Multi-round dynamic game decision-making of UAVs based on decision tree

doi:10.23919/JSEE.2025.000078

Journal of Systems Engineering and Electronics ›› 2025, Vol. 36 ›› Issue (4): 1006-1016.doi: 10.23919/JSEE.2025.000078

• SYSTEMS ENGINEERING • Previous Articles

Multi-round dynamic game decision-making of UAVs based on decision tree

Linmeng WANG(), Yuhui WANG(), Mou CHEN(), Shulin DING()

College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China

Received:2023-02-16 Online:2025-08-18 Published:2025-09-04
Contact: Yuhui WANG E-mail:wanglm25@nuaa.edu.cn;wangyh@nuaa.edu.cn;chenmou@nuaa.edu.cn;dingsl@nuaa.edu.cn
About author:
WANG Linmeng was born in 1996. She received her B.S. degree in detection guidance and control technology from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2019. She is currently pursuing her M.S. degree in control theory and control engineering with Nanjing University of Aeronautics and Astronautics. Her research interests are decision control, game theory, and air combat decision-making. E-mail: wanglm25@nuaa.edu.cn

WANG Yuhui was born in 1980. She received her B.S. degree in electrical engineering and its automation from University of Jinan, Jinan, 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

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

DING Shulin was born in 1999. She received her B.S. degree in electrical engineering and its automation from University of Jinan, Jinan, China, in 2021. She is currently pursuing her M.S. degree in digital information in Nanjing University of Aeronautics and Astronautics. Her research interest is effectiveness evaluation of air combat decision-making. E-mail: dingsl@nuaa.edu.cn
Supported by:
This work was supported by the Major Projects for Science and Technology Innovation 2030 (2018AAA0100805).

Abstract

Abstract:

To address the confrontation decision-making issues in multi-round air combat, a dynamic game decision method is proposed based on decision tree for the confrontation of unmanned aerial vehicle (UAV) air combat. Based on game theory and the confrontation characteristics of air combat, a dynamic game process is constructed including the strategy sets, the situation information, and the maneuver decisions for both sides of air combat. By analyzing the UAV’s flight dynamics and the both sides’ information, a payment matrix is established through the situation advantage function, performance advantage function, and profit function. Furthermore, the dynamic game decision problem is solved based on the linear induction method to obtain the Nash equilibrium solution, where the decision tree method is introduced to obtain the optimal maneuver decision, thereby improving the situation advantage in the next round of confrontation. According to the analysis, the simulation results for the confrontation scenarios of multi-round air combat are presented to verify the effectiveness and advantages of the proposed method.

Key words: unmanned aerial vehicle (UAV), multi-round confrontation, dynamic game decision, decision tree

Linmeng WANG, Yuhui WANG, Mou CHEN, Shulin DING. Multi-round dynamic game decision-making of UAVs based on decision tree[J]. Journal of Systems Engineering and Electronics, 2025, 36(4): 1006-1016.

Figures/Tables 15

Fig 1

Fig 2

Table 1

Table 2

Fig 3

Fig 4

Fig 5

Table 3

Table 4

Table 5

Table 6

Fig 6

Fig 7

Fig 8

Fig 9

References 35

1	WANG M L, WANG L X, YUE T, et al Influence of unmanned combat aerial vehicle agility on shortrange aerial combat effectiveness. Aerospace Science and Technology, 2020, 96, 105534. doi: 10.1016/j.ast.2019.105534
2	PIAO H Y, HAN Y, CHEN H C, et al Complex relationship graph abstraction for autonomous air combat collaboration: a learning and expert knowledge hybrid approach. Expert Systems with Applications, 2023, 215, 119285. doi: 10.1016/j.eswa.2022.119285
3	WANG Y, CAI M, JIAN X L. Consensus model of social network group decision-making based on trust relationship among experts and expert reliability. Journal of Systems Engineering and Electronics, 2023, 34(6): 1576−1588.
4	SILVER D, SCHRITTWIESER J, SIMONYAN K, et al Mastering the game of go without human knowledge. Nature, 2017, 550 (7676): 354- 359. doi: 10.1038/nature24270
5	CHEN X Y, JIANG N, JING Y W, et al Force resource complementary via lanchester square law equation. IFAC Proceedings Volumes, 2011, 44 (1): 14229- 14233. doi: 10.3182/20110828-6-IT-1002.01042
6	ZHANG J D, YU Y F, ZHENG L H, et al Situational continuity-based air combat autonomous maneuvering decision-making. Defence Technology, 2023, 29, 66- 79. doi: 10.1016/j.dt.2022.08.010
7	YANG K W, LI J C, LIU M D, et al. Complex systems and network science: a survey. Journal of Systems Engineering and Electronics, 2023, 34(3): 543−573.
8	WANG Y X. Power data mining based on deep learning and transfer learning. Hangzhou: Zhejiang University, 2019. (in Chinese)
9	ZHU J Y, KUANG M C, ZHOU W Q, et al Mastering air combat game with deep reinforcement learning. Defence Technology, 2024, 34, 295- 312. doi: 10.1016/j.dt.2023.08.019
10	TANG Z T, SHAO K, ZHAO D B, et al Recent progress of deep learning: from Alpha Go to AlphaGo Zero. Control Theory and Application, 2017, 34 (12): 1529- 1546.
11	VIRTANEN K, KARELAHTI J, RAIVIO T Modeling air combat by a moving horizon influence diagram game. Journal of Guidance, Control, and Dynamics, 2006, 29, 1080- 1091. doi: 10.2514/1.17168
12	LI B, LIANG S Y, CHEN D Q, et al A decision-making method for air combat maneuver based on hybrid deep learning network. Chinese Journal of Electronics, 2022, 31 (1): 107- 115.
13	REN Z, ZHANG D, TANG S, et al Cooperative maneuver decision making for multi-UAV air combat based on incomplete information dynamic game. Defence Technology, 2023, 27, 308- 317. doi: 10.1016/j.dt.2022.10.008
14	LI S Y, CHEN M, WANG Y H, et al Air combat decision-making of multiple UCAVs based on constraint strategy games. Defence Technology, 2022, 18 (3): 368- 383. doi: 10.1016/j.dt.2021.01.005
15	HAMBLING D AI outguns a human fighter pilot. New Scientist, 2020, 247 (3297): 12. doi: 10.1016/S0262-4079(20)31477-9
16	ZHANG J D, YANG Q M, SHI G Q, et al UAV cooperative air combat maneuver decision based on multi-agent reinforcement learning. Journal of Systems Engineering and Electronics, 2021, 32 (6): 1421- 1438. doi: 10.23919/JSEE.2021.000121
17	RAMTEKE V, COMANDUR V, MAKKAPATI V R, et al A game-theoretic model for one-on-one air combat. IFAC-Papers Online, 2022, 55 (22): 261- 267. doi: 10.1016/j.ifacol.2023.03.044
18	LI S H, DING Y, GAO Z L UAV air combat maneuvering decision based on intuitionistic fuzzy game theory. Systems Engineering and Electronics, 2019, 41 (5): 1063- 1070.
19	QIU L J, YE W. A study on the system structure of multi-UCAV cooperation mission planning. Proc. of the 10th World Congress on Intelligent Control and Automation, 2012: 4030−4034.
20	CHAO T, WANG X T, WANG S Y, et al Linear-quadratic and norm-bounded differential game combined guidance strategy against active defense aircraft in three-player engagement. Chinese Journal of Aeronautics, 2023, 36 (8): 331- 350. doi: 10.1016/j.cja.2023.04.012
21	LI Y, QIU X H, LIU X D, et al Deep reinforcement learning and its application in autonomous fitting optimization for attack areas of UCAVs. Journal of Systems Engineering and Electronics, 2020, 31 (4): 734- 742. doi: 10.23919/JSEE.2020.000048
22	HAMED D, VISAR F, MOHAMMAD J, et al. Applications of decision tree and random forest as tree-based machine learning techniques for analyzing the ultimate strain of spliced and non-spliced reinforcement bars. Applied Sciences, 2022, 12(10): 4851.
23	MENG X F, ZHANG P, XU Y, et al. Construction of decision tree based on C4.5 algorithm for online voltage stability assessment. International Journal of Electrical Power & Energy Systems, 2020, 118: 105793.
24	HUANG C Q, DONG K S, HUANG H Q, et al Autonomous air combat maneuver decision using bayesian inference and moving horizon optimization. Journal of Systems Engineering and Electronics, 2018, 29 (1): 86- 97. doi: 10.21629/JSEE.2018.01.09
25	TSAI M H, WANG H C, LEE G W, et al A decision tree based classifier to analyze human ovarian cancer cDNA microarray datasets. Journal of Medical Systems, 2016, 40 (1): 21. doi: 10.1007/s10916-015-0361-9
26	LI Y F, SHI J P, JIANG W, et al Autonomous maneuver decision-making for a UCAV in short-range aerial combat based on an MS-DDQN algorithm. Defence Technology, 2022, 18, 1697- 1714. doi: 10.1016/j.dt.2021.09.014
27	HU X X, MA H W, YE Q S, et al Hierarchical method of task assignment for multiple cooperating UAV teams. Journal of Systems Engineering and Electronics, 2015, 26 (5): 1000- 1009. doi: 10.1109/JSEE.2015.00109
28	JIANG C S, DING Q X, WANG J G, et al Research on threat assessment and target distribution for multi-aircraft cooperative air combat. Fire Control & Command Control, 2008, 33 (11): 8- 12, 21.
29	CHEN X, LI G Y, ZHAO L Research on UCAV game strategy of cooperative air combat task. Fire Control & Command Control, 2018, 43 (11): 17- 23.
30	SUN C, ZHAO H, WANG X F, et al Application of interval numbers decision in UCAV attack-defends game theory. Computer Engineering and Applications, 2017, 53 (15): 170- 175, 180.
31	AN Y B, ZHOU H S Short term effect evaluation model of rural energy construction revitalization based on ID3 decision tree algorithm. Energy Reports, 2022, 8, 1004- 1012.
32	KORI G S, KAKKASAGERI M S Classification and regression tree (CART) based resource allocation scheme for wireless sensor networks. Computer Communications, 2023, 197, 242- 254. doi: 10.1016/j.comcom.2022.11.003
33	RUAN W Y, DUAN H B, DENG Y M Autonomous maneuver decisions via transfer learning pigeoninspired optimization for UCAVs in dogfight engagements. IEEE/CAA Journal of Automatica Sinica, 2022, 9, 1639- 1657. doi: 10.1109/JAS.2021.1004269
34	ZHANG T, LI C C, MA D Y, et al An optimal task management and control scheme for military operations with dynamic game strategy. Aerospace Science and Technology, 2021, 115, 106815. doi: 10.1016/j.ast.2021.106815
35	MI X M, LIAO H C, ZENG X J, et al The two-person and zero-sum matrix game with probabilistic linguistic information. Information Sciences, 2021, 570, 487- 499. doi: 10.1016/j.ins.2021.05.019

Input attribute	Number
$ ({x_R},{y_R},{z_R}) $	$ {e_1} $
$ {V_R} $	$ {e_2} $
$ {\eta _R} $	$ {e_3} $
$ {\psi _R} $	$ {e_4} $
$ ({x_B},{y_B},{z_B}) $	$ {e_5} $
$ {V_B} $	$ {e_6} $
$ {\eta _B} $	$ {e_7} $
$ {\psi _B} $	$ {e_8} $

Output attribute	Number
Straight flight	$ {w_1} $
Turn left	$ {w_2} $
Turn right	$ {w_3} $
Accelerated flight	$ {w_4} $
Slow down flight	$ {w_5} $
Dive	$ {w_6} $
Climb	$ {w_7} $

Red side’s part strategy	Blue side’s part strategy
R₁ attacks B₁，R₂ attacks B₁ ($ {x_1} $)	B₁ attacks R₁，B₂ attacks R₁，B₃ attacks R₁，B₄ attacks R₁ ($ {y_1} $)
R₁ attacks B₁，R₂ attacks B₂ ($ {x_2} $)	B₁ attacks R₁，B₂ attacks R₁，B₃ attacks R₁，B₄ attacks R₂ ($ {y_2} $)
R₁ attacks B₁，R₂ attacks B₃ ($ {x_3} $)	B₁ attacks R₁，B₂ attacks R₁，B₃ attacks R₂，B₄ attacks R₁ ($ {y_3} $)
R₁ attacks B₁，R₂ attacks B₄ ($ {x_4} $)	B₃ attacks R₁，B₂ attacks R₁，B₃ attacks R₂，B₄ attacks R₂ ($ {y_4} $)

Red side	$ ({x_R},{y_R},{z_R}) $/$ {\mathrm{km}} $	$ {V_R} $/($ {\mathrm{m}} \cdot {{\mathrm{s}}^{ - 1}} $)	$ {\eta _R} $/$ (^{\circ} ) $	$ {\psi _R} $/$ (^{\circ} ) $
R₁	(5,15,6.0)	165	15	20
R₂	(25,10,7.0)	160	10	15

Blue side	$ ({x_B},{y_B},{z_B}) $/$ {\mathrm{km}} $	$ {V_B} $/($ {\mathrm{m}} \cdot {{\mathrm{s}}^{ - 1}} $)	$ {\eta _B} $/$ (^{\circ}) $	$ {\psi _B} $/$ (^{\circ}) $
B₁	(40,30,6.0)	160	13	165
B₂	(35,36,7.0)	155	12	170
B₃	(36,35,6.2)	160	14	175
B₄	(38,38,5.8)	158	11	168

Multi-round dynamic game decision-making of UAVs based on decision tree

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

Share this article

Figures/Tables 15

References 35

Related Articles 15

Recommended Articles

Metrics

Comments

Round number	Expected payoff
1	−0.110
5	−0.118
9	−0.098
13	0.004

[1]	Jingfeng GUO, Rui SONG, Shiwei HE. Aerial-ground collaborative delivery route planning with UAV energy function and multi-delivery [J]. Journal of Systems Engineering and Electronics, 2025, 36(2): 446-461.
[2]	Yuelong LUO, Xiuqiang JIANG, Suchuan ZHONG, Yuandong JI. Air-to-ground reconnaissance-attack task allocation for heterogeneous UAV swarm [J]. Journal of Systems Engineering and Electronics, 2025, 36(1): 155-175.
[3]	Jingfeng GUO, Rui SONG, Shiwei HE. Vehicle and onboard UAV collaborative delivery route planning: considering energy function with wind and payload [J]. Journal of Systems Engineering and Electronics, 2025, 36(1): 194-208.
[4]	Guang ZHAN, Kun ZHANG, Ke LI, Haiyin PIAO. UAV maneuvering decision-making algorithm based on deep reinforcement learning under the guidance of expert experience [J]. Journal of Systems Engineering and Electronics, 2024, 35(3): 644-665.
[5]	Jiandong ZHANG, Yukun GUO, Lihui ZHENG, Qiming YANG, Guoqing SHI, Yong WU. Real-time UAV path planning based on LSTM network [J]. Journal of Systems Engineering and Electronics, 2024, 35(2): 374-385.
[6]	Boyu QIN, Dong ZHANG, Shuo TANG, Yang XU. Two-layer formation-containment fault-tolerant control of fixed-wing UAV swarm for dynamic target tracking [J]. Journal of Systems Engineering and Electronics, 2023, 34(6): 1375-1396.
[7]	Jianhong WANG, RAMIREZ-MENDOZA Ricardo A., Yang XU. Nonlinear direct data-driven control for UAV formation flight system [J]. Journal of Systems Engineering and Electronics, 2023, 34(6): 1409-1418.
[8]	Zhiwen XIAO, Xiaowei FU. A cooperative detection game: UAV swarm vs. one fast intruder [J]. Journal of Systems Engineering and Electronics, 2023, 34(6): 1565-1575.
[9]	Jie LI, Xiaoyu DANG, Sai LI. DQN-based decentralized multi-agent JSAP resource allocation for UAV swarm communication [J]. Journal of Systems Engineering and Electronics, 2023, 34(2): 289-298.
[10]	Yaozhong ZHANG, Yike LI, Zhuoran WU, Jialin XU. Deep reinforcement learning for UAV swarm rendezvous behavior [J]. Journal of Systems Engineering and Electronics, 2023, 34(2): 360-373.
[11]	Xing LEI, Xiaoxuan HU, Guoqiang WANG, He LUO. A multi-UAV deployment method for border patrolling based on Stackelberg game [J]. Journal of Systems Engineering and Electronics, 2023, 34(1): 99-116.
[12]	Hao LI, Hemin SUN, Ronghua ZHOU, Huainian ZHANG. Hybrid TDOA/FDOA and track optimization of UAV swarm based on A-optimality [J]. Journal of Systems Engineering and Electronics, 2023, 34(1): 149-159.
[13]	Weikun HE, Jingbo SUN, Xinyun ZHANG, Zhenming LIU. Micro-Doppler feature extraction of micro-rotor UAV under the background of low SNR [J]. Journal of Systems Engineering and Electronics, 2022, 33(6): 1127-1139.
[14]	Yang XU, Weiming ZHENG, Delin LUO, Haibin DUAN. Dynamic affine formation control of networked under-actuated quad-rotor UAVs with three-dimensional patterns [J]. Journal of Systems Engineering and Electronics, 2022, 33(6): 1269-1285.
[15]	Honghong ZHANG, Xusheng GAN, Shuangfeng LI, Zhiyuan CHEN. UAV safe route planning based on PSO-BAS algorithm [J]. Journal of Systems Engineering and Electronics, 2022, 33(5): 1151-1160.