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Partial component consensus of leader-following multi-agent systems

## Partial component consensus of leader-following multi-agent systems

Wu Bin-Bin, Ma Zhong-Jun, Wang Yi
• #### Abstract

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.

#### Authors and contacts

###### 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).

#### References

 [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]

#### Cited By

•  [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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•  Citation:
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• Abstract views:  554
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##### Publishing process
• Received Date:  29 June 2016
• Accepted Date:  30 November 2016
• Published Online:  20 March 2017

## Partial component consensus of leader-following multi-agent systems

###### Corresponding author: Ma Zhong-Jun, mzj1234402@163.com;
• 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
Fund Project:  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).

Abstract: 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.

Reference (19)

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