领导-跟随多智能体系统的部分分量一致性

吴彬彬; 马忠军; 王毅

doi:10.7498/aps.66.060201

摘要

首先给出多智能体系统的部分分量一致性概念，然后探讨有向网络拓扑结构下的一阶非线性领导-跟随多智能体系统的部分分量一致性问题.通过设计合适的牵引控制器，建立相应的误差系统，将多智能体系统的部分分量一致性转化为误差系统的部分变元稳定性，并运用矩阵理论和稳定性理论，导出该多智能体系统实现部分分量一致性的充分条件.数值模拟验证了理论结果的正确性.

关键词:

Consensus problems, as basic topics in distributed coordination of multi-agent systems, have drawn a great deal of attention from different research fields. Generally, consensus refers to the asymptotic convergence of state variables of all agents with time evolution. In this paper, a concept on partial component consensus in multi-agent system is first given, which is a weaker dynamic behavior of group than the consensus in general, and then the problem of partial component consensus in leader-following first-order multi-agent system with the directed network topology is discussed. By designing an appropriate pinning control protocol and building corresponding error system, partial component consensus in multi-agent system is transformed into the partial variable stability of the error system. Using matrix theory and stability theory, a sufficient condition is given to realize partial component consensus in multi-agent system. Numerical simulations are given to illustrate the theoretical results.

Keywords:

作者及机构信息

1.
桂林电子科技大学数学与计算科学学院, 桂林 541004;

2.
桂林电子科技大学, 广西高校数据分析与计算重点实验室, 桂林 541004;

3.
浙江财经大学数学与统计学院, 杭州 310012

通信作者: 马忠军, mzj1234402@163.com

基金项目: 国家自然科学基金（批准号：11562006，61663006）、广西自然科学基金（批准号：2015GXNSFAA139013）、桂林电子科技大学研究生教育创新计划（批准号：YJCXS201555）、广西优秀中青年骨干教师培养工程项目（批准号：gxqg022014025）和浙江省自然科学基金（批准号：LY17A020007）资助的课题.

Authors and contacts

1.
School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China;

2.
Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, China;

3.
School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310012, China

Corresponding author: Ma Zhong-Jun, mzj1234402@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11562006, 61663006), the Natural Science Foundation of Guangxi, China (Grant No. 2015GXNSFAA139013), the Innovation Project of GUET Graduate Education, China (Grant No. YJCXS201555), the Outstanding Young Teachers Training in Higher Education Institutions of Guangxi, China (Grant No. gxqg022014025), and the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY17A020007).

参考文献

[1]	Vicsek T, Czirok A, Ben-Jacob E, Cohen I, Shochet O 1995 Phys. Rev. Lett. 75 1226
[2]	Jadbabaie A, Lin J, Morse A S 2003 IEEE Trans. Autom. Control 48 988
[3]	Qu Z H, Wang J, Hull R A 2008 IEEE Trans. Autom. Control 53 894
[4]	Cortes J, Bullo F 2005 SIAM J. Control Optimization 44 1543
[5]	Wang N, Wu Z H, Peng L 2014 Chin. Phys. B 23 108901
[6]	Fax J A, Murray R M 2004 IEEE Trans. Autom. Control 49 1465
[7]	Olfati-Saber R, Murray R M 2004 IEEE Trans. Autom. Control 49 1520
[8]	Guo L X, Hu M F, Hu A H, Xu Z Y 2014 Chin. Phys. B 23 050508
[9]	Ji L H, Liao X F 2012 Acta Phys. Sin. 61 150202 (in Chinese) [纪良浩, 廖晓峰 2012 物理学报 61 150202]
[10]	Xie D S, Xie J Q, Zhao H Y 2015 Proceedings of the 34 Chinese Control Conference Hangzhou, China, July 28-30, 2015 p7529
[11]	Yu W W, Chen G R, Cao M, Kurths J 2010 Automatica 46 1089
[12]	Xin Y M, Li Y X, Huang X, Cheng Z S 2015 Neurocomputing 159 84
[13]	Yu W W, Chen G R, Cao M 2011 IEEE Trans. Autom. Control 56 1436
[14]	Zhao Y, Li B, Qin J H, Gao H J, Karimi H R 2013 IEEE Trans. Cybernet. 43 2157
[15]	Saadi P T, Mardani M M, Shasadeghi M, Safarinezhadian B 2015 4th Iranian Joint Congress on Fuzzy and Intelligent Systems Zahedan, Iran, September 9-11, 2015 p1
[16]	Ni W, Cheng D Z 2010 System Control Lett. 59 209
[17]	Xie Y Y, Wang Y, Ma Z J 2014 Acta Phys. Sin. 63 040202 (in Chinese) [谢媛艳, 王毅, 马忠军 2014 物理学报 63 040202]
[18]	Xiao F, Wang L, Chen J 2010 System Control Lett. 59 775
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施引文献

[1]	Vicsek T, Czirok A, Ben-Jacob E, Cohen I, Shochet O 1995 Phys. Rev. Lett. 75 1226
[2]	Jadbabaie A, Lin J, Morse A S 2003 IEEE Trans. Autom. Control 48 988
[3]	Qu Z H, Wang J, Hull R A 2008 IEEE Trans. Autom. Control 53 894
[4]	Cortes J, Bullo F 2005 SIAM J. Control Optimization 44 1543
[5]	Wang N, Wu Z H, Peng L 2014 Chin. Phys. B 23 108901
[6]	Fax J A, Murray R M 2004 IEEE Trans. Autom. Control 49 1465
[7]	Olfati-Saber R, Murray R M 2004 IEEE Trans. Autom. Control 49 1520
[8]	Guo L X, Hu M F, Hu A H, Xu Z Y 2014 Chin. Phys. B 23 050508
[9]	Ji L H, Liao X F 2012 Acta Phys. Sin. 61 150202 (in Chinese) [纪良浩, 廖晓峰 2012 物理学报 61 150202]
[10]	Xie D S, Xie J Q, Zhao H Y 2015 Proceedings of the 34 Chinese Control Conference Hangzhou, China, July 28-30, 2015 p7529
[11]	Yu W W, Chen G R, Cao M, Kurths J 2010 Automatica 46 1089
[12]	Xin Y M, Li Y X, Huang X, Cheng Z S 2015 Neurocomputing 159 84
[13]	Yu W W, Chen G R, Cao M 2011 IEEE Trans. Autom. Control 56 1436
[14]	Zhao Y, Li B, Qin J H, Gao H J, Karimi H R 2013 IEEE Trans. Cybernet. 43 2157
[15]	Saadi P T, Mardani M M, Shasadeghi M, Safarinezhadian B 2015 4th Iranian Joint Congress on Fuzzy and Intelligent Systems Zahedan, Iran, September 9-11, 2015 p1
[16]	Ni W, Cheng D Z 2010 System Control Lett. 59 209
[17]	Xie Y Y, Wang Y, Ma Z J 2014 Acta Phys. Sin. 63 040202 (in Chinese) [谢媛艳, 王毅, 马忠军 2014 物理学报 63 040202]
[18]	Xiao F, Wang L, Chen J 2010 System Control Lett. 59 775
[19]	Liao X X 2001 Mathematical Theory of Stability and Its Application (Wuhan: Central China Normal University Press) pp19, 321, 336 (in Chinese) [廖晓昕 2001 稳定性的数学理论及应用 (武汉: 华中师范大学出版社) 第19, 321, 336页]

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