多智能体系统二分一致性的研究进展

唐宏安; 夏紫怡; 王丽丹; 段书凯

doi:10.16383/j.aas.c240530

多智能体系统二分一致性的研究进展

doi: 10.16383/j.aas.c240530 cstr: 32138.14.j.aas.c240530

唐宏安^1,,
夏紫怡^1,,
王丽丹^{2, 3, 4, 5,},
段书凯^{2, 3, 4, 5,}

1.
重庆理工大学两江人工智能学院重庆 401135
2.
西南大学人工智能学院重庆 400715
3.
智能传动和控制技术国家地方联合工程研究中心重庆 400715
4.
类脑计算与智能芯片重庆市重点实验室重庆 400715
5.
发光分析与分子传感教育部重点实验室重庆 400715

基金项目: 西南大学创新研究2035先导计划重点研发项目(SWU-XDZD22009), 国家自然科学基金(U20A20227, 62076207, 62076208, 62402298), 重庆英才计划(CQYC20210302257), 重庆市教委科学技术研究项目(KJQN202304109)资助

详细信息

作者简介:
唐宏安：重庆理工大学两江人工智能学院讲师. 2020年获得西南大学计算智能与信息处理专业博士学位. 主要研究方向为多智能体系统协同控制, 智能控制, 人工智能和耦合忆阻神经网络. E-mail: tanghongan163@163.com

夏紫怡：重庆理工大学两江人工智能学院硕士研究生. 主要研究方向为多智能体系统协同控制, 智能控制和耦合忆阻神经网络. E-mail: xiaziyi0329@163.com

王丽丹：西南大学人工智能学院教授. 2008年获得重庆大学计算机软件与理论专业博士学位. 主要研究方向为忆阻器件与系统, 混沌系统与非线性电路设计, 深度学习和数字图像处理. E-mail: ldwang@swu.edu.cn

段书凯：西南大学人工智能学院教授. 2006年获得重庆大学计算机科学专业博士学位. 主要研究方向为人工智能, 类脑芯片, 工业机器人, 智能控制和仿生信息材料. 本文通信作者. E-mail: duansk@swu.edu.cn

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出版历程
- 收稿日期: 2024-07-27
- 录用日期: 2024-11-21
- 网络出版日期: 2025-01-25

Research Progress on Bipartite Consensus of Multi-agent Systems

TANG Hong-An^1
,,
XIA Zi-Yi^1
,,
WANG Li-Dan^{2, 3, 4, 5
,},
DUAN Shu-Kai^{2, 3, 4, 5
,}

1.
School of Artificial Intelligence, Chongqing University of Technology, Chonqing 401135
2.
College of Artificial Intelligence, Southwest University, Chonqing 400715
3.
National and Local Joint Engineering Research Center of Intelligent Transmission and Control Technology, Chonqing 400715
4.
Chongqing Key Laboratory of Brain-inspired Computing and Intelligent Chips, Chonqing 400715
5.
Key Laboratory of Luminescence Analysis and Molecular Sensing, Ministry of Education, Chongqing 400715

Funds: Supported by Key Project of Innovation Research 2035 Pilot Plan of Southwest University (SWU-XDZD22009), National Natural Science Foundation of China (U20A20227, 62076207, 62076208, 62402298), Chongqing Talent Plan (CQYC20210302257), and the Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN202304109)

More Information

Author Bio:
TANG Hong-An　Lecturer at the School of Artificial Intelligence, Chongqing University of Technology. He received his Ph.D. degree in computational intelligence and information processing from Southwest University in 2020. His research interest covers coordination control of multi-agent systems, intelligent control, artificial intelligence, and coupled memristive neural networks

XIA Zi-Yi　Master student at the School of Artificial Intelligence, Chongqing University of Technology. Her research interest covers coordination control of multi-agent systems, intelligent control, and coupled memristive neural networks

WANG Li-Dan　Professor at the College of Artificial Intelligence, Southwest University. She received her Ph.D. degree in computer software and theory from Chongqing University in 2008. Her research interest covers memristive devices and systems, chaotic systems and nonlinear circuit design, deep learning, and digital image processing

DUAN Shu-Kai　Professor at the College of Artificial Intelligence, Southwest University. He received his Ph.D. degree in computer science from Chongqing University in 2006. His research interest covers artificial intelligence, brain-inspired chips, industrial robots, intelligent control, and bionic information materials. Corresponding author of this paper

摘要

摘要: 多智能体系统是分布式人工智能的重要分支, 通过智能体之间的交互与协作完成复杂的任务. 一致性是协同控制的核心问题, 二分一致性作为一致性的延伸受到了广泛关注. 首先, 介绍一些符号图知识, 给出一阶、二阶、高阶及分数阶多智能体系统的模型及一些二分一致性的定义. 其次, 概述这四类多智能体系统多种二分一致性的研究进展. 此外, 分析有限时间、固定时间和预设时间二分一致性的优势及保守性, 讨论二分一致性和二分输出一致性的特点. 最后, 对多智能体系统二分一致性进行总结与展望.
- 二分一致性 /
- 二分输出一致性 /
- 符号图 /
- 多智能体系统
Abstract: As an important branch of distributed artificial intelligence, multi-agent systems achieve complex tasks through interaction and collaboration among agents. Consensus is the core issue of collaborative control. Bipartite consensus has received widespread attention since it is an extension of consensus. Firstly, this paper introduces some knowledge of signed graph and provides models for first-order, second-order, high-order, and fractional-order multi-agent systems, as well as some definitions of bipartite consensus. Secondly, the research progress on multiple bipartite consensus of these four types of multi-agent systems is summarized. In addition, it analyzes the advantages and conservatism of finite-time, fixed-time, and predefined-time bipartite consensus and discusses the characteristics of bipartite consensus and bipartite output consensus. Finally, the summary and outlook on bipartite consensus of multi-agent systems are provided.
- Bipartite consensus /
- bipartite output consensus /
- signed graph /
- multi-agent systems

HTML全文

图 1 多智能体系统(3)的拓扑图

Fig. 1 Topology graph of multi-agent system (3)

下载: 全尺寸图片幻灯片

图 2 $w_{i1}(t)$的状态轨迹, $i=1,\;2,\;\cdots,\;7$

Fig. 2 State trajectories of $w_{i1}(t)$, $i=1,\;2,\;\cdots,\;7$

下载: 全尺寸图片幻灯片

图 4 $w_{i2}(t)$的状态轨迹, $i=1,\;2,\;\cdots,\;7$

Fig. 4 State trajectories of $w_{i2}(t)$, $i=1,\;2,\;\cdots,\;7$

下载: 全尺寸图片幻灯片

图 3 $v_{11}(t)$的变化过程

Fig. 3 The process of change in $v_{11}(t)$

下载: 全尺寸图片幻灯片

图 5 $v_{12}(t)$的变化过程

Fig. 5 The process of change in $v_{12}(t)$

下载: 全尺寸图片幻灯片

表 1 多智能体系统二分一致性文献总结

Table 1 Summary of literature on bipartite consensus of multi-agent systems

二分一致性类型	一阶多智能体系统	二阶多智能体系统	高阶多智能体系统	分数阶多智能体系统
渐近二分一致性	[54	[92−98]	[109−113]	[119−121]
有限时间二分一致性	[60−61]	[99−102]
固定时间二分一致性	[67−73]	[32−33]	[37]
预设时间二分一致性	[76−77]	[33, 103−104]	[38]
渐近二分输出一致性	[81−88]	[34]	[116]	[46]

下载: 导出CSV

参考文献(121)

[1]	Mushtaq A, Ul Haq I, Sarwar M A, Khan A, Khalil W, Mughal M A. Multi-agent reinforcement learning for traffic flow management of autonomous vehicles. Sensors, 2023, 23(5): Article No. 2373 doi: 10.3390/s23052373
[2]	Lotfy A, Chaoui H, Kandidayeni M, Boulon L. Enhancing energy management strategy for battery electric vehicles: Incorporating cell balancing and multi-agent twin delayed deep deterministic policy gradient architecture. IEEE Transactions on Vehicular Technology, 2024, 73(11): 16593−16607 doi: 10.1109/TVT.2024.3427683
[3]	虞逸凡. 基于深度强化学习的多智能体编队避障控制研究 [硕士学位论文], 大连海洋大学, 中国, 2024. Yu Yi-Fan. Research on Multi-agent Formation and Obstacle Avoidance Control Based on Deep Reinforcement Learning [Master thesis], Dalian Ocean University, China, 2024.
[4]	胡翔, 熊余, 张祖凡. DOS攻击下饱和脉冲多智能体系统的安全定制化一致性. 自动化学报, 2024, 50(12): 2499−2512 Hu Xiang, Xiong Yu, Zhang Zu-Fan. Security customization consensus of multi-agent systems based on saturation impulse under DOS attacks. Acta Automatica Sinica, 2024, 50(12): 2499−2512
[5]	Wang J Y, Zhang H G, Wang Z S, Fu J, Wang W, Meng Q G. Event-triggered leader-following consensus control of nonlinear multiagent systems with generally uncertain Markovian switching topologies. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2024, 54(8): 4942−4954 doi: 10.1109/TSMC.2024.3389689
[6]	杨东岳, 梅杰. 有向图中基于扰动观测器的线性多智能体系统一致性. 自动化学报, 2018, 44(6): 1037−1044 Yang Dong-Yue, Mei Jie. Disturbance observer based consensus of linear multi-agent systems under a directed graph. Acta Automatica Sinica, 2018, 44(6): 1037−1044
[7]	吴彭磊. 多智能体网络的一致性问题及编队控制研究 [硕士学位论文], 北京交通大学, 中国, 2020. Wu Peng-Lei. Research on Consensus Problem and Formation Control of Multi-agent Network [Master thesis], Beijing Jiaotong University, China, 2020.
[8]	Wang F, Zhang C, Li N, Yang Y Q. On leaderless consensus of incommensurate order multi-agent systems. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 2024, 238(5): 957−966 doi: 10.1177/09596518231204053
[9]	Chen L K, Guo L X, Yang Y Q. Projective group consensus of multi-agent systems with arbitrary parameter. Journal of Systems Science and Complexity, 2021, 34(2): 618−631 doi: 10.1007/s11424-020-9137-5
[10]	Ma Y J, Li Z J, Xie X P, Yue D. Adaptive consensus of uncertain switched nonlinear multi-agent systems under sensor deception attacks. Chaos, Solitons & Fractals, 2023, 175: Article No. 113936
[11]	Xu N, Chen Z Y, Niu B, Zhao X D. Event-triggered distributed consensus tracking for nonlinear multi-agent systems: A minimal approximation approach. IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 2023, 13(3): 767−779 doi: 10.1109/JETCAS.2023.3277544
[12]	Zhang K, Zhou B, Duan G R. Leader-following consensus of multi-agent systems with time delays by fully distributed protocols. Systems & Control Letters, 2023, 178: Article No. 105582
[13]	Yang Y P, Shen B, Han Q L. Dynamic event-triggered scaled consensus of multi-agent systems in reliable and unreliable networks. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2024, 54(2): 1124−1136 doi: 10.1109/TSMC.2023.3324142
[14]	Geng H, Wu H Y, Miao J L, Hou S, Chen Z Q. Consensus of heterogeneous multi-agent systems under directed topology. IEEE Access, 2022, 10: 5936−5943 doi: 10.1109/ACCESS.2022.3142539
[15]	Ma C Q, Zhao W W, Zhao Y B. Bipartite consensus of discrete-time double-integrator multi-agent systems with measurement noise. Journal of Systems Science and Complexity, 2018, 31(6): 1525−1540 doi: 10.1007/s11424-018-7363-x
[16]	Zhang H W, Chen J. Bipartite consensus of multi-agent systems over signed graphs: State feedback and output feedback control approaches. International Journal of Robust and Nonlinear Control, 2017, 27(1): 3−14 doi: 10.1002/rnc.3552
[17]	Zhang X X, Liu X P, Lewis F L, Wang X. Bipartite tracking consensus of nonlinear multi-agent systems. Physica A: Statistical Mechanics and Its Applications, 2020, 545: Article No. 123504 doi: 10.1016/j.physa.2019.123504
[18]	Liu C, Li R, Liu B. Group-bipartite consensus of heterogeneous multi-agent systems over signed networks. Physica A: Statistical Mechanics and Its Applications, 2022, 592: Article No. 126712 doi: 10.1016/j.physa.2021.126712
[19]	Sun Y S, Ji Z J, Qi Q Y, Ma H Z. Bipartite consensus of multi-agent systems with intermittent interaction. IEEE Access, 2019, 7: 130300−130311 doi: 10.1109/ACCESS.2019.2940541
[20]	陈世明, 姜根兰, 张正. 通信受限的多智能体系统二分实用一致性. 自动化学报, 2022, 48(5): 1318−1326 Chen Shi-Ming, Jiang Gen-Lan, Zhang Zheng. Bipartite practical consensus control of multi-agent systems with communication constraints. Acta Automatica Sinica, 2022, 48(5): 1318−1326
[21]	Wang L, Chen G W, Li T, Yang R T. Fully distributed, event-triggered containment control of multi-agent systems based on wireless sensor networks and time base generators. Applied Sciences, 2023, 13(19): Article No. 11039 doi: 10.3390/app131911039
[22]	Okereke C E, Mohamad M M, Wahab N H A, Elijah O, Al-Nahari A, Zaleha H S. An overview of machine learning techniques in local path planning for autonomous underwater vehicles. IEEE Access, 2023, 11: 24894−24907 doi: 10.1109/ACCESS.2023.3249966
[23]	Bogue R. The role of robots in environmental monitoring. Industrial Robot: The International Journal of Robotics Research and Application, 2023, 50(3): 369−375 doi: 10.1108/IR-12-2022-0316
[24]	Wang Q F, Wang Z S, Ma L. Adaptive finite-time bipartite consensus of multi-agent systems with communication link uncertainty under signed digraph. Neurocomputing, 2024, 598: Article No. 128012 doi: 10.1016/j.neucom.2024.128012
[25]	Guo X, Liang J L, Lu J Q. Finite-time asymmetric bipartite consensus for signed networks of dynamic agents. International Journal of Control, Automation and Systems, 2019, 17(4): 1041−1049 doi: 10.1007/s12555-018-0360-y
[26]	Yang S F, Xing P F, Li G B, Tao J. Nonlinear fixed-time bipartite consensus algorithm for multiagent systems. In: Proceedings of the 33rd Chinese Control and Decision Conference (CCDC). Kunming, China: IEEE, 2021. 4509−4513
[27]	Wu Y, Hu S W, Chen X Y, Zhao F. Prescribed-time bipartite average consensus of multi-agent systems with cooperative-competitive interactions. In: Proceedings of the 13th Asian Control Conference (ASCC). Jeju, Republic of Korea: IEEE, 2022. 1210−1214
[28]	Geng X T, Feng J W, Wang J Y, Li N, Zhao Y. Prespecified-time bipartite consensus of multi-agent systems via intermittent control. IEEE Transactions on Circuits and Systems I: Regular Papers, 2024, 71(5): 2240−2251 doi: 10.1109/TCSI.2024.3350248
[29]	Duan J, Zhang H G, Liang Y L, Cai Y L. Bipartite finite-time output consensus of heterogeneous multi-agent systems by finite-time event-triggered observer. Neurocomputing, 2019, 365: 86−93 doi: 10.1016/j.neucom.2019.07.043
[30]	Zhang H G, Duan J, Wang Y C, Gao Z Y. Bipartite fixed-time output consensus of heterogeneous linear multiagent systems. IEEE Transactions on Cybernetics, 2021, 51(2): 548−557 doi: 10.1109/TCYB.2019.2936009
[31]	吴佳慧, 朱韵茹, 郑元世, 王怀柱. 二阶混杂多智能体系统的安全二分一致性. 控制理论与应用, 2023, 40(10): 1821−1830 doi: 10.7641/CTA.2022.20099 Wu Jia-Hui, Zhu Yun-Ru, Zheng Yuan-Shi, Wang Huai-Zhu. Secure bipartite consensus of second-order hybrid multi-agent systems. Control Theory & Applications, 2023, 40(10): 1821−1830 doi: 10.7641/CTA.2022.20099
[32]	Zhao X F, Han T, Xiao B, Zhan X S, Yan H C. Finite-time and fixed-time bipartite consensus tracking for second-order multi-agent systems via an integral sliding-mode approach. International Journal of Control, Automation and Systems, 2023, 21(12): 3922−3931 doi: 10.1007/s12555-022-0174-9
[33]	Wang S, Zhan X S, Wu J, Cheng L L, Wu B. Fixed-time and predefined-time bipartite consensus tracking for second-order multi-agent systems based on sliding-mode approach. Circuits, Systems, and Signal Processing, 2024, 43(11): 6855−6873 doi: 10.1007/s00034-024-02774-3
[34]	Hu H X, Wen G H, Chen G, Chen Y, Yu X H. Output bipartite consensus for second-order heterogeneous uncertain agents with state-dependent cooperation-competition interactions. IEEE Transactions on Control of Network Systems, 2023, 10(2): 912−925 doi: 10.1109/TCNS.2022.3212014
[35]	Valcher M E, Misra P. On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions. Systems & Control Letters, 2014, 66: 94−103
[36]	Wang Q, Zhong W M, Xu J P, He W L, Tan D Y. Bipartite tracking consensus control of nonlinear high-order multi-agent systems subject to exogenous disturbances. IEEE Access, 2019, 7: 145910−145920 doi: 10.1109/ACCESS.2019.2944759
[37]	Yang H J, Ye D. Adaptive fixed-time bipartite tracking consensus control for unknown nonlinear multi-agent systems: An information classification mechanism. Information Sciences, 2018, 459: 238−254 doi: 10.1016/j.ins.2018.04.016
[38]	Li K, Hua C C, You X, Ahn C K. Output feedback predefined-time bipartite consensus control for high-order nonlinear multiagent systems. IEEE Transactions on Circuits and Systems I: Regular Papers, 2021, 68(7): 3069−3078 doi: 10.1109/TCSI.2021.3071974
[39]	Ma H W, Liu D R, Wang D, Luo B. Bipartite output consensus in networked multi-agent systems of high-order power integrators with signed digraph and input noises. International Journal of Systems Science, 2016, 47(13): 3116−3131 doi: 10.1080/00207721.2015.1090039
[40]	Wu Z S, Zhang X X, Wang J H, Zeng X Y. Applications of fractional differentiation matrices in solving Caputo fractional differential equations. Fractal and Fractional, 2023, 7(5): Article No. 374 doi: 10.3390/fractalfract7050374
[41]	梁渊哲, 任全彬, 何高让, 郜婕, 王新彤. 基于分数阶三参数模型的HTPB推进剂粘弹性力学响应分析. 固体火箭技术, 2024, 47(2): 173−180 doi: 10.7673/j.issn.1006-2793.2024.02.004 Liang Yuan-Zhe, Ren Quan-Bin, He Gao-Rang, Gao Jie, Wang Xin-Tong. Viscoelastic mechanical response analysis of HTPB propellant based on fractional-order three-parameter model. Journal of Solid Rocket Technology, 2024, 47(2): 173−180 doi: 10.7673/j.issn.1006-2793.2024.02.004
[42]	韦婷. 分数阶多智能体系统的协同控制 [硕士学位论文], 电子科技大学, 中国, 2023. Wei Ting. Cooperative Control of Fractional-order Multi-agent Systems [Master thesis], University of Electronic Science and Technology of China, China, 2023.
[43]	周杰. 基床沥青混凝土层全温度域动力特性与结构设计研究 [博士学位论文], 东南大学, 中国, 2021. Zhou Jie. Research on Dynamic Characteristics and Structural Design of Asphalt Concrete Layer in Railway Substructure within Full Temperature Range [Ph.D. dissertation], Southeast University, China, 2021.
[44]	冯桂珍, 赵东鹏, 李韶华. 基于分数阶的空气弹簧建模及电动汽车主动悬架控制研究. 汽车工程, 2024, 46(7): 1282−1293 Feng Gui-Zhen, Zhao Dong-Peng, Li Shao-Hua. Research on air spring modeling based on fractional order and electric vehicle active suspension control. Automotive Engineering, 2024, 46(7): 1282−1293
[45]	Shahvali M, Azarbahram A, Naghibi-Sistani M B, Askari J. Bipartite consensus control for fractional-order nonlinear multi-agent systems: An output constraint approach. Neurocomputing, 2020, 397: 212−223 doi: 10.1016/j.neucom.2020.02.036
[46]	Mahmoodi H, Shojaei K. Adaptive bipartite output consensus of nonlinear fractional-order multi-agent systems. International Journal of Systems Science, 2022, 53(8): 1615−1638 doi: 10.1080/00207721.2021.2019345
[47]	Ning B D, Han Q L, Zuo Z Y, Ding L, Lu Q, Ge X H. Fixed-time and prescribed-time consensus control of multiagent systems and its applications: A survey of recent trends and methodologies. IEEE Transactions on Industrial Informatics, 2023, 19(2): 1121−1135 doi: 10.1109/TII.2022.3201589
[48]	Wang Y M, Lin H, Lam J, Kwok K W. Differentially private consensus and distributed optimization in multi-agent systems: A review. Neurocomputing, 2024, 597: Article No. 127986 doi: 10.1016/j.neucom.2024.127986
[49]	Amirkhani A, Barshooi A H. Consensus in multi-agent systems: A review. Artificial Intelligence Review, 2022, 55(5): 3897−3935 doi: 10.1007/s10462-021-10097-x
[50]	Ma L F, Wang Z D, Han Q L, Liu Y R. Consensus control of stochastic multi-agent systems: A survey. Science China Information Sciences, 2017, 60(12): Article No. 120201 doi: 10.1007/s11432-017-9169-4
[51]	张栋, 马苏慧, 吕石, 王孟阳, 唐硕. 多智能体系统事件触发一致性研究综述. 北京理工大学学报, 2022, 42(10): 1059−1072 Zhang Dong, Ma Su-Hui, Lv Shi, Wang Meng-Yang, Tang Shuo. Overview on event-triggered consensus of multi-agent systems. Transactions of Beijing Institute of Technology, 2022, 42(10): 1059−1072
[52]	Liang J Q, Bu X H, Cui L Z, Hou Z S. Event-triggered asymmetric bipartite consensus tracking for nonlinear multi-agent systems based on model-free adaptive control. IEEE/CAA Journal of Automatica Sinica, 2023, 10(3): 662−672 doi: 10.1109/JAS.2022.106070
[53]	Xu Z Q, Li C D, Li Y, Han Y Y, Hu X. Bipartite consensus of nonlinear discrete-time multi-agent systems via variable impulsive control. International Journal of Control, Automation and Systems, 2022, 20(2): 461−471 doi: 10.1007/s12555-020-0792-z
[54]	王君, 韦娅萍. 分布式事件触发下的多智能体系统二分一致性. 兰州理工大学学报, 2024, 50(3): 77−83 Wang Jun, Wei Ya-Ping. Bipartite consensus of multi-agent systems triggered by distributed events. Journal of Lanzhou University of Technology, 2024, 50(3): 77−83
[55]	Mondal S, Tsourdos A. Asymmetric bipartite consensus of nonlinear agents with communication noise. Journal of Intelligent & Robotic Systems, 2023, 109(1): Article No. 8
[56]	Tian H H, Wang P J, Huang T W. Bipartite consensus of multi-agent systems with a non-autonomous leader under directed switching signed graphs. IEEE Transactions on Circuits and Systems II: Express Briefs, 2024, 71(3): 1161−1165
[57]	Ren J, Hua L, Zhao M, Lu G P. Bipartite consensus for multi-agent systems over signed networks: A novel dynamic event-triggered mechanism. Neurocomputing, 2024, 609: Article No. 128502 doi: 10.1016/j.neucom.2024.128502
[58]	Guo X, Lu J Q, Alsaedi A, Alsaadi F E. Bipartite consensus for multi-agent systems with antagonistic interactions and communication delays. Physica A: Statistical Mechanics and Its Applications, 2018, 495: 488−497 doi: 10.1016/j.physa.2017.12.078
[59]	Yu J J, Yu J S, Zhang P F, Yang T T, Chen X R. A unified framework design for finite-time bipartite consensus of multi-agent systems. IEEE Access, 2021, 9: 48971−48979 doi: 10.1109/ACCESS.2021.3069337
[60]	Guo W L, He W N, Sun W, Lu X Q. Robust finite-time and fixed-time bipartite consensus problems for multi-agent systems via discontinuous protocol. International Journal of Control, 2022, 95(2): 380−389 doi: 10.1080/00207179.2020.1797177
[61]	Gao S, Wen G G, Zhai X Q, Zheng P. Finite-/fixed-time bipartite consensus for first-order multi-agent systems via impulsive control. Applied Mathematics and Computation, 2023, 442: Article No. 127740 doi: 10.1016/j.amc.2022.127740
[62]	Chen X, Zhao L, Yu J P. Adaptive neural finite-time bipartite consensus tracking of nonstrict feedback nonlinear coopetition multi-agent systems with input saturation. Neurocomputing, 2020, 397: 168−178 doi: 10.1016/j.neucom.2020.02.054
[63]	Liang J Q, Bu X H, Cui L Z, Hou Z S. Finite time asymmetric bipartite consensus for multi-agent systems based on iterative learning control. International Journal of Robust and Nonlinear Control, 2021, 31(12): 5708−5724 doi: 10.1002/rnc.5568
[64]	Chen X Y, Yang X, Li J J, Wang Y J, Chen Q. Practical finite-time bipartite consensus for nonlinear multi-agent systems under antagonistic interactions and actuation failures. In: Proceedings of the 6th International Symposium on Autonomous Systems (ISAS). Nanjing, China: IEEE, 2023. 1−6
[65]	Wang X, Wang S D, Liu J, Wu Y B, Sun C Y. Bipartite finite-time consensus of multi-agent systems with intermittent communication via event-triggered impulsive control. Neurocomputing, 2024, 598: Article No. 127970 doi: 10.1016/j.neucom.2024.127970
[66]	Liang J Q, Bu X H, Hou Z S. Finite-time asymmetric bipartite consensus for multi-agent systems using data-driven iterative learning control. IEEE Transactions on Signal and Information Processing Over Networks, 2024, 10: 227−238 doi: 10.1109/TSIPN.2024.3375602
[67]	李振涛, 冯元珍, 王正新. 事件触发下多智能体系统固定时间二分一致性. 计算机工程与应用, 2021, 57(21): 80−86 doi: 10.3778/j.issn.1002-8331.2010-0170 Li Zhen-Tao, Feng Yuan-Zhen, Wang Zheng-Xin. Fixed-time bipartite consensus of multi-agent systems via event-triggered control. Computer Engineering and Applications, 2021, 57(21): 80−86 doi: 10.3778/j.issn.1002-8331.2010-0170
[68]	Zhang W, Huang Q, Alhudhaif A. Event-triggered fixed-time bipartite consensus for nonlinear disturbed multi-agent systems with leader-follower and leaderless controller. Information Sciences, 2024, 662: Article No. 120243 doi: 10.1016/j.ins.2024.120243
[69]	Zhao M, Peng C, Tian E G. Finite-time and fixed-time bipartite consensus tracking of multi-agent systems with weighted antagonistic interactions. IEEE Transactions on Circuits and Systems I: Regular Papers, 2021, 68(1): 426−433 doi: 10.1109/TCSI.2020.3027327
[70]	Deng Q, Wu J, Han T, Yang Q S, Cai X S. Fixed-time bipartite consensus of multi-agent systems with disturbances. Physica A: Statistical Mechanics and Its Applications, 2019, 516: 37−49 doi: 10.1016/j.physa.2018.09.066
[71]	Li B X, Han T, Xiao B, Zhan X S, Yan H C. Adaptive controller design for fixed-time bipartite consensus of multi-agent systems with disturbances. International Journal of Adaptive Control and Signal Processing, 2022, 36(9): 2305−2318 doi: 10.1002/acs.3459
[72]	王啸, 刘剑, 武永宝, 孙长银. 对抗网络下时滞非线性多智能体系统固定时间二分一致性. 控制理论与应用, 2023, 40(2): 204−211 doi: 10.7641/CTA.2022.11280 Wang Xiao, Liu Jian, Wu Yong-Bao, Sun Chang-Yin. Fixed-time bipartite consensus of delayed nonlinear multi-agent systems under antagonistic network. Control Theory & Applications, 2023, 40(2): 204−211 doi: 10.7641/CTA.2022.11280
[73]	Xu Z, Liu X Y, Cao J D, Song M. Fixed-time bipartite consensus of nonlinear multi-agent systems under directed signed graphs with disturbances. Journal of the Franklin Institute, 2022, 359(6): 2693−2709 doi: 10.1016/j.jfranklin.2022.02.023
[74]	马小陆, 谭毅波, 梅宏. 符号图下含扰动的多智能体系统预定时间二分一致性. 控制与决策, 2024, 39(5): 1517−1526 Ma Xiao-Lu, Tan Yi-Bo, Mei Hong. Predefined-time bipartite consensus of multi-agent systems with disturbances under signed graph. Control and Decision, 2024, 39(5): 1517−1526
[75]	Ren C E, Zhang J A, Guan Y. Prescribed performance bipartite consensus control for stochastic nonlinear multiagent systems under event-triggered strategy. IEEE Transactions on Cybernetics, 2023, 53(1): 468−482 doi: 10.1109/TCYB.2021.3119066
[76]	Gong X, Cui Y K, Shen J, Shu Z, Huang T W. Distributed prescribed-time interval bipartite consensus of multi-agent systems on directed graphs: Theory and experiment. IEEE Transactions on Network Science and Engineering, 2021, 8(1): 613−624 doi: 10.1109/TNSE.2020.3047232
[77]	Chen X, Yu H, Hao F. Prescribed-time event-triggered bipartite consensus of multiagent systems. IEEE Transactions on Cybernetics, 2022, 52(4): 2589−2598 doi: 10.1109/TCYB.2020.3004572
[78]	Zang J P, Chen X. Practical prescribed-time event-triggered bipartite consensus of linear multi-agent systems. IEEE Access, 2020, 8: 199664−199672 doi: 10.1109/ACCESS.2020.3035420
[79]	Han C L, Qin K Y, Shi M J, Liu Y, Li W H, Lin B X. Prescribed time bipartite output consensus tracking for heterogeneous multi-agent systems with external disturbances. Applied Mathematics and Computation, 2024, 469: Article No. 128550 doi: 10.1016/j.amc.2024.128550
[80]	Zuo S, Lewis F L, Song Y D, Davoudi A. Bipartite output synchronization of heterogeneous multiagent systems on signed digraphs. International Journal of Robust and Nonlinear Control, 2018, 28(13): 4017−4031 doi: 10.1002/rnc.4118
[81]	Zhang H G, Cai Y L, Wang Y C, Su H G. Adaptive bipartite event-triggered output consensus of heterogeneous linear multiagent systems under fixed and switching topologies. IEEE Transactions on Neural Networks and Learning Systems, 2020, 31(11): 4816−4830 doi: 10.1109/TNNLS.2019.2958107
[82]	Duan J, Zhang H G, Han J, Gao Z Y. Bipartite output consensus of heterogeneous linear multi-agent systems by dynamic triggering observer. ISA Transactions, 2019, 92: 14−22 doi: 10.1016/j.isatra.2019.02.020
[83]	Ma Q, Zhou G P, Li E Y. Adaptive bipartite output consensus of heterogeneous linear multi-agent systems with antagonistic interactions. Neurocomputing, 2020, 373: 50−55 doi: 10.1016/j.neucom.2019.09.067
[84]	Han T, Zheng W X. Bipartite output consensus for heterogeneous multi-agent systems via output regulation approach. IEEE Transactions on Circuits and Systems II: Express Briefs, 2021, 68(1): 281−285
[85]	Zhang X X, Liu X P, Sun Y S. Bipartite output consensus for heterogeneous multi-agent systems via reduced-order observer-based protocols. Neurocomputing, 2020, 406: 274−281 doi: 10.1016/j.neucom.2020.04.006
[86]	Lu M Y, Han T, Wu J, Zhan X S, Yan H C. Adaptive bipartite output consensus for heterogeneous multi-agent systems via state/output feedback control. IEEE Transactions on Circuits and Systems II: Express Briefs, 2022, 69(8): 3455−3459
[87]	Zhang L Z, Li Y Y, Lu J Q, Lou J G. Bipartite event-triggered impulsive output consensus for switching multi-agent systems with dynamic leader. Information Sciences, 2022, 612: 414−426 doi: 10.1016/j.ins.2022.08.086
[88]	Mu R, Wei A R, Li H T, Zhang X F, Qi Y A. Bipartite output consensus for heterogeneous multi-agent systems with observer-based adaptive event-triggered strategy. IEEE Systems Journal, 2023, 17(4): 6011−6021
[89]	Cai Y L, Zhang H G, Liu Y, He Q. Distributed bipartite finite-time event-triggered output consensus for heterogeneous linear multi-agent systems under directed signed communication topology. Applied Mathematics and Computation, 2020, 378: Article No. 125162 doi: 10.1016/j.amc.2020.125162
[90]	Xiang K L, Yu Z Y, Jiang H J. Fixed-time bipartite output consensus of heterogeneous multi-agent systems with event-triggered observation. IEEE Access, 2023, 11: 31188−31198 doi: 10.1109/ACCESS.2023.3262284
[91]	刘沛明, 郭祥贵. 基于观测器的人在环多机械臂系统预设性能二分一致性. 自动化学报, 2024, 50(9): 1761−1771 Liu Pei-Ming, Guo Xiang-Gui. Observer-based prescribed performance bipartite consensus for human-in-the-loop multi-manipulator systems. Acta Automatica Sinica, 2024, 50(9): 1761−1771
[92]	Shao J L, Shi L, Zhang Y Z, Cheng Y H. On the asynchronous bipartite consensus for discrete-time second-order multi-agent systems with switching topologies. Neurocomputing, 2018, 316: 105−111 doi: 10.1016/j.neucom.2018.07.056
[93]	Miao S X, Su H S. Bipartite consensus for second-order multiagent systems with matrix-weighted signed network. IEEE Transactions on Cybernetics, 2022, 52(12): 13038−13047 doi: 10.1109/TCYB.2021.3097056
[94]	Xu H C, Liu C, Lv Y, Zhou J L. Adaptive bipartite consensus of second-order multi-agent systems with bounded disturbances. IEEE Access, 2020, 8: 186441−186447 doi: 10.1109/ACCESS.2020.3028096
[95]	Zhou B L, Yang Y Q, Li L, Xu X Y, Yang R T. Bipartite consensus for second-order multi-agent systems with external disturbances via constraint data-sampled impulsive method. Communications in Nonlinear Science and Numerical Simulation, 2022, 109: Article No. 106314 doi: 10.1016/j.cnsns.2022.106314
[96]	Wu J, Deng Q, Chen C Y, Yan H C. Bipartite consensus for second order multi-agent systems with exogenous disturbance via pinning control. IEEE Access, 2019, 7: 186563−186571 doi: 10.1109/ACCESS.2019.2959719
[97]	Wang X, Liu J, Wu Y B, Sun C Y. Dynamic event-triggered leader-following bipartite consensus of second-order multi-agent systems under DoS attacks. International Journal of Robust and Nonlinear Control, 2024, 34(15): 10731−10749 doi: 10.1002/rnc.7543
[98]	罗香, 冯元珍. DoS攻击下二阶多智能体系统二分跟踪一致性. 计算机工程与应用, 2023, 59(12): 77−83 doi: 10.3778/j.issn.1002-8331.2207-0192 Luo Xiang, Feng Yuan-Zhen. Bipartite consensus tracking of second-order multi-agent systems under DoS attacks. Computer Engineering and Applications, 2023, 59(12): 77−83 doi: 10.3778/j.issn.1002-8331.2207-0192
[99]	Zhao L, Jia Y M, Yu J P. Adaptive finite-time bipartite consensus for second-order multi-agent systems with antagonistic interactions. Systems & Control Letters, 2017, 102: 22−31
[100]	Lu R X, Wu J, Zhan X S, Yan H C. Finite-time group-bipartite consensus tracking for second-order nonlinear multi-agent systems. Neurocomputing, 2023, 545: Article No. 126283 doi: 10.1016/j.neucom.2023.126283
[101]	Lu R X, Wu J, Zhan X S, Yan H C. Finite-time bipartite consensus for second-order nonlinear multi-agent systems under random switching topologies. IEEE Transactions on Circuits and Systems II: Express Briefs, 2023, 70(12): 4474−4478
[102]	Zhou Y C, Yang Y Q, Chang Q, Xu X Y. Intermittent event-triggered control for finite-time bipartite consensus of second-order multi-agent systems. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 2022, 236(7): 1255−1273 doi: 10.1177/09596518221088444
[103]	王婧. 考虑执行器故障的多智能体系统滑模容错一致性控制研究 [硕士学位论文], 燕山大学, 中国, 2023. Wang Jing. Research on Sliding-mode Fault-tolerant Consensus Control for Multi-agent Systems With Actuator Faults [Master thesis], Yanshan University, China, 2023.
[104]	Ren Y H, Chen Z W, Ji Y, Li Z W. Predefined-time bipartite tracking consensus for second-order multi-agent systems with cooperative and antagonistic networks. Journal of Control and Decision, 2023, 10(2): 280−292 doi: 10.1080/23307706.2022.2063956
[105]	卫强强, 刘蓉, 张衡. 四旋翼无人机高阶一致性编队控制方法. 电光与控制, 2019, 26(8): 1−5 doi: 10.3969/j.issn.1671-637X.2019.08.001 Wei Qiang-Qiang, Liu Rong, Zhang Heng. A high-order consensus based formation control algorithm of quadrotor UAVs. Electronics Optics & Control, 2019, 26(8): 1−5 doi: 10.3969/j.issn.1671-637X.2019.08.001
[106]	李桂璞. 高阶多智能体系统的非线性一致性与分布式优化算法研究 [博士学位论文], 东南大学, 中国, 2020. Li Gui-Pu. Research on Nonlinear Consensus and Distributed Optimization Algorithms of Higher-order Multi-agent Systems [Ph.D. dissertation], Southeast University, China, 2020.
[107]	Ren S Y, Mao R, Wu J G. Passivity-based leader-following consensus control for nonlinear multi-agent systems with fixed and switching topologies. IEEE Transactions on Network Science and Engineering, 2019, 6(4): 844−856 doi: 10.1109/TNSE.2018.2876262
[108]	Wang Q, Wang J L, Wu H N, Huang T W. Consensus and H_∞ consensus of nonlinear second-order multi-agent systems. IEEE Transactions on Network Science and Engineering, 2020, 7(3): 1251−1264 doi: 10.1109/TNSE.2019.2917287
[109]	Shi L, Chen L L, Cheng Y H. High-order bipartite consensus for multiagent systems over signed networks subject to asynchronous communications. IEEE Transactions on Network Science and Engineering, 2021, 8(4): 3325−3334
[110]	Wu Y Z, Zhao Y Y, Hu J P. Bipartite consensus control of high-order multiagent systems with unknown disturbances. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 49(10): 2189−2199 doi: 10.1109/TSMC.2017.2761362
[111]	Qi Y A, Zhang X F, Mu R, Chang Y J. Bipartite consensus for high-order nonlinear multi-agent systems via event-triggered/self-triggered control. Systems & Control Letters, 2023, 172: Article No. 105439
[112]	Zhang L L, Liu S S, Hua C C. Distributed bipartite containment control of high-order nonlinear multi-agent systems with time-varying powers. IEEE Transactions on Circuits and Systems I: Regular Papers, 2023, 70(3): 1371−1380 doi: 10.1109/TCSI.2022.3225207
[113]	Xu Y L, Wang J H, Zhang Y W, Xu Y. Event-triggered bipartite consensus for high-order multi-agent systems with input saturation. Neurocomputing, 2020, 379: 284−295 doi: 10.1016/j.neucom.2019.10.095
[114]	Guo W L, Shi L L, Sun W, Jahanshahi H. Predefined-time average consensus control for heterogeneous nonlinear multi-agent systems. IEEE Transactions on Circuits and Systems II: Express Briefs, 2023, 70(8): 2989−2993
[115]	付璐, 陈霞, 郭晓亚. 有向图下的多智能体系统事件触发预设时间实用一致性. 自动化与仪表, 2024, 39(5): 20−25 Fu Lu, Chen Xia, Guo Xiao-Ya. Event-triggered predefined-time practical consensus for multi-agent systems under directed graph. Automation & Instrumentation, 2024, 39(5): 20−25
[116]	Zhao L, Yu J P, Lin C. Command filter based adaptive fuzzy bipartite output consensus tracking of nonlinear coopetition multi-agent systems with input saturation. ISA Transactions, 2018, 80: 187−194 doi: 10.1016/j.isatra.2018.07.039
[117]	Shahvali M, Shojaei K. Distributed adaptive neural control of nonlinear multi-agent systems with unknown control directions. Nonlinear Dynamics, 2016, 83(4): 2213−2228 doi: 10.1007/s11071-015-2476-4
[118]	Wang W, Wang D, Peng Z H. Distributed containment control for uncertain nonlinear multi-agent systems in non-affine pure-feedback form under switching topologies. Neurocomputing, 2015, 152: 1−10 doi: 10.1016/j.neucom.2014.11.035
[119]	Gong P. Exponential bipartite consensus of fractional-order non-linear multi-agent systems in switching directed signed networks. IET Control Theory & Applications, 2020, 14(17): 2582−2591
[120]	Yang X Y, Cao J D, Liu H, Huang C D, Xue G M. Composite adaptive fuzzy bipartite consensus of fractional-order multiagent systems with a switched event-triggered mechanism. ISA Transactions, 2024, 148: 224−236 doi: 10.1016/j.isatra.2024.02.033
[121]	潘丹. 分数阶时滞非线性多智能体系统的二分一致性及跟踪控制 [硕士学位论文], 杭州电子科技大学, 中国, 2023. Pan Dan. Bipartite Consensus and Tracking Control of Fractional-order Nonlinear Multi-agent Systems With Delays [Master thesis], Hangzhou Dianzi University, China, 2023.