系统工程与电子技术 ›› 2023, Vol. 45 ›› Issue (9): 2852-2859.doi: 10.12305/j.issn.1001-506X.2023.09.24
谢震海1,2, 何明1, 禹明刚1,*, 余烤华1, 袁国栋1
收稿日期:
2022-04-03
出版日期:
2023-08-30
发布日期:
2023-09-05
通讯作者:
禹明刚
作者简介:
谢震海(1988—), 男, 硕士研究生, 主要研究方向为无人化指挥控制基金资助:
Zhenhai XIE1,2, Ming HE1, Minggang YU1,*, Kaohua YU1, Guodong YUAN1
Received:
2022-04-03
Online:
2023-08-30
Published:
2023-09-05
Contact:
Minggang YU
摘要:
针对无人集群自主协同时作战单元策略选择多样性问题,基于无标度网络,引入公共物品博弈理论,改进愿景驱动机制,构建无人集群合作演化模型。首先,理论推导出集群作战单元总效能解析表达式。然后,仿真分析多样性策略选择情况下,收益系数、愿景水平、策略数量、成本等各类参数变化对无人集群合作水平的影响。最后,据此给出无人集群作战中有效应对多样性选择的合理建议,为无人集群的自组织协同提供决策支持,为有关理论研究转变为实际军事应用提供理论支持。
中图分类号:
谢震海, 何明, 禹明刚, 余烤华, 袁国栋. 面向策略多样性的无人集群合作演化建模及仿真[J]. 系统工程与电子技术, 2023, 45(9): 2852-2859.
Zhenhai XIE, Ming HE, Minggang YU, Kaohua YU, Guodong YUAN. Modeling and simulation of cooperative evolution of unmanned swarms for strategy diversity[J]. Systems Engineering and Electronics, 2023, 45(9): 2852-2859.
表2
参数映射关系"
序号 | 参数(变量) | 含义 | 现实意义 |
1 | N | 结构种群 | 无人集群 |
2 | kx | 个体x的度 | 无人作战单元的邻居个数 |
3 | r | 增益因子 | 无人作战单元在参与合作时的收益翻倍系数 |
4 | Cx | 个体参与每个集群投资量 | 无人作战单元在与它相邻的所有作战单元(邻居所属的集群)合作时的支付 |
5 | fx | 个体x在博弈中的一次收益 | 某无人作战单元在以其邻居为中心的集群中的一次合作收益 |
6 | fx, y | 个体x在以个体y为中心的集群博弈收益 | 无人作战单元x为焦点, 在与以作战单元y为中心的集群中合作后, 作战单元x的收益 |
7 | Fx | 个体x的博弈收益 | 同一作战单元在多方多策略合作和的具体收益 |
8 | si | 策略 | 无人作战单元愿意向集群贡献资源的合作行为 |
9 | ω | 选择强度 | 无人作战单元在战场中选择策略的活跃度 |
10 | α | 愿景水平 | 无人作战单元在合作时自身根据战场环境选择策略的期望度 |
11 | S | 策略集 | 参与合作博弈的无人作战平台的所有行为数量 |
1 |
张婷婷, 蓝羽石, 宋爱国. 无人集群系统自主协同技术综述[J]. 指挥与控制学报, 2021, 7 (2): 127- 136.
doi: 10.3969/j.issn.2096-0204.2021.02.0127 |
ZHANG T T , LAN Y S , SONG A G . An overview of autonomous collaboration technologies for unmanned swarm systems[J]. Journal of Command and Control, 2021, 7 (2): 127- 136.
doi: 10.3969/j.issn.2096-0204.2021.02.0127 |
|
2 | 王婧玥. 公共物品博弈中社会价值取向和对方合作性对合作行为的影响[D]. 上海: 华东师范大学, 2020. |
WANG J Y. The influence of social value orientation and cooperation on cooperative behavior in public goods game[D]. Shanghai: East China Normal University, 2020. | |
3 |
LI S W , WANG C . Network structure, portfolio diversification and systemic risk[J]. Journal of Management Science and Engineering, 2021, 6 (2): 235- 245.
doi: 10.1016/j.jmse.2021.06.006 |
4 |
LI C , MAINI P K . An evolving network model with community structure[J]. Journal of Physics A: Mathematical and General, 2005, 38 (45): 9741- 9749.
doi: 10.1088/0305-4470/38/45/002 |
5 | 任林涛, 裴忠民, 熊伟, 等. 考虑节点负载的多社团网络级联失效问题研究[J]. 计算机工程与应用, 2022, 58 (6): 95- 102. |
REN L T , PEI Z M , XIONG W , et al. Research on cascading failure of multi-community network considering node load[J]. Computer Engineering and Applications, 2022, 58 (6): 95- 102. | |
6 | 闫晓雪, 纪志坚. 社交网络中多领导者观点的博弈建模分析[J]. 复杂系统与复杂性科学, 2022, 19 (1): 20-26, 73. |
YAN X X , JI Z J . Game modeling analysis of multi-leaders opinion in social network[J]. Complex Systems and Complexity Science, 2022, 19 (1): 20-26, 73. | |
7 |
LI L , LIU Y P , HE K X . Meteorological satellite stakeholder relationship network based on social network analysis[J]. Systems Engineering and Electronics, 2021, 32 (4): 907- 926.
doi: 10.23919/JSEE.2021.000078 |
8 | ZHANG J L , ZHU Y Y , CHEN Z Q . Evolutionary game dynamics of multiagent systems on multiple community networks[J]. IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2018, 50 (11): 4513- 4529. |
9 | 禹明刚, 何明, 张东戈, 等. 基于多元公共品演化博弈的无人作战集群策略占优条件[J]. 系统工程与电子技术, 2021, 43 (9): 2553- 2561. |
YU M G , HE M , ZHANG D G , et al. Strategy dominance condition of unmanned combat cluster based on multi-player public goods evolutionary game[J]. Systems Engineering and Electronics, 2021, 43 (9): 2553- 2561. | |
10 | DU J M , WU B , WANG L . Aspiration dynamics and the sustainability of resources in the public goods dilemma[J]. Physics Letters A, 2016, 380 (16): 432- 1436. |
11 | 苏奇. 复杂网络上的合作演化和博弈动力学研究[D]. 北京: 北京大学, 2020: 2-10. |
SU Q. Cooperative evolution and game dynamics on complex networks[D]. Beijing: Peking University, 2020: 2-10. | |
12 | FLORES L S , FERNANDES H , AMARAL M A , et al. Symbiotic behaviour in the public goods game with altruistic punishment[J]. Journal of Theoretical Biology, 2021, 524 (6): 110737. |
13 | WOLFF I . What are the equilibria in public-good experiments[J]. Economics Letters, 2017, 150 (1): 83- 85. |
14 |
SANTOS F C , SANTOS M D , PACHECO J M . Social diversity promotes the emergence of cooperation in public goods games[J]. Nature, 2008, 454 (7201): 213- 216.
doi: 10.1038/nature06940 |
15 |
SZABÓ G , HAUERT C . Phase transitions and volunteering in spatial public goods games[J]. Physical Review Letters, 2002, 89 (11): 118101.
doi: 10.1103/PhysRevLett.89.118101 |
16 |
WAKANO J Y . A mathematical analysis on public goods games in the continuous space[J]. Mathematical Biosciences, 2006, 201 (1-2): 72- 89.
doi: 10.1016/j.mbs.2005.12.015 |
17 |
FOTOUHI B , MOMENI N , ALLEN B , et al. Evolution of cooperation on large networks with community structure[J]. Journal of the Royal Society Interface, 2019, 16 (152): 20180677.
doi: 10.1098/rsif.2018.0677 |
18 | JOSEF T , ANDREAS P , KRISHNENDU C , et al. Population structure determines the tradeoff between fixation probability and fixation time[J]. Communications Biology, 2019, 12 (1): 138. |
19 |
ALLEN B , LIPPNER G , NOWAK M A . Evolutionary games on isothermal graphs[J]. Nature Communications, 2019, 10 (1): 5107.
doi: 10.1038/s41467-019-13006-7 |
20 |
HAUERT C . Volunteering as red queen mechanism for coope-ration in public goods games[J]. Science, 2002, 296 (5570): 1129- 1132.
doi: 10.1126/science.1070582 |
21 | GUAN J Y , WU Z X , WANG Y H . Effects of inhomogeneous activity of players and noise on cooperation in spatial public goods games[J]. Physical Review E, 2007, 76 (5Pt 2): 056101. |
22 | SZABO G , ANTAL T , SZABO P , et al. Spatial evolutionary prisoner's dilemma game with three strategies and external constraints[J]. Physical Review E Statistical Physics Plasmas Fluids & Related Interdisciplinary Topics, 2000, 62 (1): 1095- 1103. |
23 | SZABO G , VUKOV J . Cooperation for volunteering and partially random partnerships[J]. Physical Review E Statistical Nonlinear & Soft Matter Physics, 2004, 69 (3): 036107. |
24 |
AKÇAY E . Deconstructing evolutionary game theory: co-evolution of social behaviors with their evolutionary setting[J]. The American Naturalist, 2020, 195 (2): 315- 330.
doi: 10.1086/706811 |
25 |
LI Z H , WANG B H , LIU R R , et al. Evolutionary prisoner's dilemma game based on division of work[J]. Chinese Physics Letters, 2009, 26 (10): 108701.
doi: 10.1088/0256-307X/26/10/108701 |
26 | 李艳. 网络上的多策略演化动力学研究[D]. 南京: 南京航空航天大学, 2015. |
LI Y. Research on multi strategy evolution dynamics on networks[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2015. | |
27 | YE W X , FAN S H . Evolutionary snowdrift game with rational selection based on radical evaluation[J]. Applied Mathematics & Computation, 2017, 294 (C): 310- 317. |
28 |
ZHANG H B , WANG H . Group preferential selection promotes cooperation in spatial public goods game[J]. International Journal of Modern Physics C, 2014, 25 (11): 1450062.
doi: 10.1142/S0129183114500624 |
29 | SHI D M , ZHUANG Y , WANG B H . Group diversity promotes cooperation in the spatial public goods game[J]. Europhysics Letters, 2010, 90 (5): 1632- 1652. |
30 | SHI D M , ZHUANG Y , LI Y J , et al. Depreciation of public goods in spatial public goods games[J]. Journal of Statistical Mechanics Theory & Experiment, 2011, 2011 (10): 10007. |
31 |
SHI D M . Effect of the depreciation of public goods in spatial public goods games-science direct[J]. Physica A: Statistical Mechanics and its Applications, 2012, 391 (4): 1636- 1641.
doi: 10.1016/j.physa.2011.10.006 |
32 |
DU J M , WU B , WANG L . Aspiration dynamics in structured population acts as if in a well-mixed one[J]. Scientific Reports, 2015, 5 (1): 8014.
doi: 10.1038/srep08014 |
33 |
SUI X K , CONG R , LI K , et al. Evolutionary dynamics of N-person snowdrift game[J]. Physics Letters A, 2015, 379 (45-46): 2922- 2934.
doi: 10.1016/j.physleta.2015.08.029 |
34 |
WU B , TRANLSEN A , GOKHALE C . Dynamic properties of evolutionary multi-player games in finite populations[J]. Games, 2013, 4 (2): 182- 199.
doi: 10.3390/g4020182 |
35 |
WU B , ALTROCK P M , WANG L , et al. Universality of weak selection[J]. Physical Review E, 2010, 82 (4): 046106.
doi: 10.1103/PhysRevE.82.046106 |
36 |
DU J M , WU B , ALTROCK P M , et al. Aspiration dynamics of multi-player games in finite populations[J]. Journal of the Royal Society Interface, 2014, 11 (94): 20140077.
doi: 10.1098/rsif.2014.0077 |
37 |
SU Q , WANG L , STANLEY H E . Understanding spatial public goods games on three-layer networks[J]. New Journal of Physics, 2018, 20 (10): 103030.
doi: 10.1088/1367-2630/aae6dd |
38 |
LEE K H , CHAN C H , HUI P M , et al. Cooperation in N-person evolutionary snowdrift game in scale-free Barabási-Albert networks[J]. Physica A: Statistical Mechanics and its Applications, 2008, 387 (22): 5602- 5608.
doi: 10.1016/j.physa.2008.05.045 |
39 | ZHENG D F , YIN H P , CHAN C H , et al. Cooperative behavior in a model of evolutionary snowdrift games with N-person interactions[J]. Europhysics Letters, 2008, 80 (1): 417- 429. |
40 | ZHONG L X , ZHENG D F , ZHENG B , et al. Networking effects on cooperation in evolutionary snowdrift game[J]. Europhysics Letters, 2007, 76 (4): 724. |
41 | 吕金虎, 谭少林. 复杂网络上的博弈及其演化动力学[M]. 北京: 高等教育出版社, 2019. |
LV J H , TAN S L . Games and evolutionary dynamics on complex networks[M]. Beijing: Higher Education Press, 2019. | |
42 | YU M G , HE M , MA Z Y , et al. Cooperative evolution mechanism of unmanned swarm within the framework of public goods game[J]. Mathematical Problems in Engineering, 2021, 2021 (Pt. 15): 5575815. |
43 | YU M G, HE M, ZHANG D, et al. An approach to coordinated control of structured unmanned swarm based on evolutio-nary game[C]//Proc. of the 3rd International Conference on Unmanned Systems, 2020. |
44 | 顾凌枫, 何明, 陈国友, 等. 无人机集群系统弹性研究[J]. 系统工程与电子技术, 2021, 43 (1): 162- 168. |
GU L F , HE M , CHEN G Y , et al. Research on unmanned aerial vehicle swarm system resilience[J]. Systems Engineering and Electronics, 2021, 43 (1): 162- 168. | |
45 | 刘锦涛, 何明, 罗玲, 等. 无人机集群牵制控制系统特征值分析[J]. 系统工程与电子技术, 2022, 44 (2): 612- 618. |
LIU J T , HE M , LUO L , et al. Eigenvalue analysis of the pinning control system of unmanned aerial vehicle swarm[J]. Systems Engineering and Electronics, 2022, 44 (2): 612- 618. | |
46 |
XU K Y , LI K , CONG R , et al. Cooperation guided by the coexistence of imitation dynamics and aspiration dynamics in structured populations[J]. Europhysics Letters, 2017, 117 (4): 48002.
doi: 10.1209/0295-5075/117/48002 |
47 | LIU Q , HE M , XU D , et al. A mechanism for identifying and suppressing the emergent flocking behaviors of UAV swarms[J]. Mathematical Problems in Engineering, 2018, (Pt. 11): 6734923. |
48 |
BARABASI A L , ALBERT R . Emergence of scaling in random networks[J]. Science, 1999, 286 (5439): 509- 512.
doi: 10.1126/science.286.5439.509 |
49 | KURZBAN B , HOUSER D . Individual differences in cooperation in a circular public goods game[J]. European Journal of Personality, 2010, 15 (S1): 37- 52. |
50 |
BAHBOUHI J E , MOUSSA N . Leaders rewiring mechanism promotes cooperation in public goods game[J]. International Journal of Modern Physics C, 2021, 32 (10): 2150127.
doi: 10.1142/S0129183121501278 |
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