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Group consensus analysis of multi-agent systems with delays

Ji Liang-Hao Liao Xiao-Feng Liu Qun

Group consensus analysis of multi-agent systems with delays

Ji Liang-Hao, Liao Xiao-Feng, Liu Qun
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  • In this paper, a new consensus problem is investigated which is group consensus. It contains such consensus problem as a special case that all agents in a network reach a consistent value asymptotically. Consider a dynamic multi-agent system with connected undirected or connected bipartite graph topology and delays, two novel consensus protocols are introduced to solve the group consensus problem. The convergence analysis is discussed and the sufficient condition for system group convergence is obtained based on the frequency-domain analysis and generalized Nyquist criterion, respectively. And we know that the condition of group convergence is only depended on system's time delay and the adjacent weight between the agents, meanwhile, delay can affect the dynamic characteristics of the system. Finally, simulations are provided to demonstrate the effectiveness of our theoretical results.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 60973114, 61170249), the Natural Science Foundation of CQCSTC (Grant Nos. 2009BA2024, cstc2011jjA1320), and the State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University(Grant No. 2007DA10512711206).
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    [2]

    Yu W W, Chen G R, Wang Z D, Yang W 2009 IEEE Trans. on Syst. Man Cybern. 39 1568

    [3]

    Vicsek T, Czirok A, Ben-Jacob E 1995 Phys. Rev. Lett. 75 1226

    [4]

    Jadbabaie A, Lin J, Morse A S 2003 IEEE Trans. on Autom. Control 48 988

    [5]

    Olfati-Saber R, Murray R M 2004 IEEE Trans. on Autom. Control 49 1520

    [6]

    Ren W, Beard R W 2005 IEEE Trans. on Autom. Control 50 655

    [7]

    Moreau L 2005 IEEE Trans. on Autom. Control 50 169

    [8]

    Wang W, Slotine J J E 2006 IEEE Trans. on Autom. Control 51 712

    [9]

    Tan F X, Guan X P, Liu D R 2008 Chin. Phys. B 17 3531

    [10]

    Sun Y Z, Ruan J 2008 Chin. Phys. B 17 4137

    [11]

    Bliman P A, Ferrari-Trecate G 2008 Automatica 44 1985

    [12]

    Tian Y P, Liu C L 2008 IEEE Trans. on Autom. Control 53 2122

    [13]

    Li Y M, Guan X P 2009 Chin. Phys. B 18 3355

    [14]

    Hu J P, Yuan H W 2009 Chin. Phys. B 18 3777

    [15]

    Tian Y P, Liu C L 2009 Automatica 45 1347

    [16]

    Lin P, Jia Y M 2010 IEEE Trans. on Autom. Control 55 778

    [17]

    Wang Y Z, Zhang C H, Liu Z B 2012 Automatica 10 1016

    [18]

    Xia W G, Gao M 2011 Automatica 11 2395

    [19]

    Yu J Y, Wang L 2009 Proceeding of the 7th Asian Control Conference, Hong Kong, China, August 27-29, 2001, p105

    [20]

    Yu J Y, Wang L 2012 International Journal of Systems Science 43 334

    [21]

    Yu J Y, Wang L 2009 Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, China, December 16-18, 2009, p2652

    [22]

    Yu J Y, Wang L 2010 Systems & Control Letters 59 340

    [23]

    Wang q, Wang Y Z, Yang R M 2012 Control and Decision 27 1586 (in Chinese) [王强, 王玉振, 杨仁明 2012 控制与决策 27 1586]

    [24]

    Tian Y, Yang H. 2004 Proceedings of the 5th World Congress on Intelligent Control and Automation, Hangzhou, China, June 14-15, 2004 p15

    [25]

    Yang H Y, Tian S W, Zhang S Y 2011 Acta Electronica Sinica 39 872 (in Chinese) [杨洪勇, 田生文, 张嗣瀛 2011 电子学报 39 872]

  • [1]

    Olfati-Saber R 2006 IEEE Trans. on Autom. Control 51 401

    [2]

    Yu W W, Chen G R, Wang Z D, Yang W 2009 IEEE Trans. on Syst. Man Cybern. 39 1568

    [3]

    Vicsek T, Czirok A, Ben-Jacob E 1995 Phys. Rev. Lett. 75 1226

    [4]

    Jadbabaie A, Lin J, Morse A S 2003 IEEE Trans. on Autom. Control 48 988

    [5]

    Olfati-Saber R, Murray R M 2004 IEEE Trans. on Autom. Control 49 1520

    [6]

    Ren W, Beard R W 2005 IEEE Trans. on Autom. Control 50 655

    [7]

    Moreau L 2005 IEEE Trans. on Autom. Control 50 169

    [8]

    Wang W, Slotine J J E 2006 IEEE Trans. on Autom. Control 51 712

    [9]

    Tan F X, Guan X P, Liu D R 2008 Chin. Phys. B 17 3531

    [10]

    Sun Y Z, Ruan J 2008 Chin. Phys. B 17 4137

    [11]

    Bliman P A, Ferrari-Trecate G 2008 Automatica 44 1985

    [12]

    Tian Y P, Liu C L 2008 IEEE Trans. on Autom. Control 53 2122

    [13]

    Li Y M, Guan X P 2009 Chin. Phys. B 18 3355

    [14]

    Hu J P, Yuan H W 2009 Chin. Phys. B 18 3777

    [15]

    Tian Y P, Liu C L 2009 Automatica 45 1347

    [16]

    Lin P, Jia Y M 2010 IEEE Trans. on Autom. Control 55 778

    [17]

    Wang Y Z, Zhang C H, Liu Z B 2012 Automatica 10 1016

    [18]

    Xia W G, Gao M 2011 Automatica 11 2395

    [19]

    Yu J Y, Wang L 2009 Proceeding of the 7th Asian Control Conference, Hong Kong, China, August 27-29, 2001, p105

    [20]

    Yu J Y, Wang L 2012 International Journal of Systems Science 43 334

    [21]

    Yu J Y, Wang L 2009 Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, China, December 16-18, 2009, p2652

    [22]

    Yu J Y, Wang L 2010 Systems & Control Letters 59 340

    [23]

    Wang q, Wang Y Z, Yang R M 2012 Control and Decision 27 1586 (in Chinese) [王强, 王玉振, 杨仁明 2012 控制与决策 27 1586]

    [24]

    Tian Y, Yang H. 2004 Proceedings of the 5th World Congress on Intelligent Control and Automation, Hangzhou, China, June 14-15, 2004 p15

    [25]

    Yang H Y, Tian S W, Zhang S Y 2011 Acta Electronica Sinica 39 872 (in Chinese) [杨洪勇, 田生文, 张嗣瀛 2011 电子学报 39 872]

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    [8] He Zheng-Bing, Ma Shou-Feng, He Guo-Guang. Experimental macroscopic phenomena in urban transportation system. Acta Physica Sinica, 2010, 59(1): 171-177. doi: 10.7498/aps.59.171
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    [10] Xie Yuan-Yan, Wang Yi, Ma Zhong-Jun. Delay consensus of leader-following multi-agent systems. Acta Physica Sinica, 2014, 63(4): 040202. doi: 10.7498/aps.63.040202
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  • Received Date:  17 April 2012
  • Accepted Date:  10 June 2012
  • Published Online:  20 November 2012

Group consensus analysis of multi-agent systems with delays

  • 1. State Key Lab. of Power Transmission Equipment & System Security and New Technology, College of Computer Science, Chongqing University,Chongqing 400044, China;
  • 2. College of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 60973114, 61170249), the Natural Science Foundation of CQCSTC (Grant Nos. 2009BA2024, cstc2011jjA1320), and the State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University(Grant No. 2007DA10512711206).

Abstract: In this paper, a new consensus problem is investigated which is group consensus. It contains such consensus problem as a special case that all agents in a network reach a consistent value asymptotically. Consider a dynamic multi-agent system with connected undirected or connected bipartite graph topology and delays, two novel consensus protocols are introduced to solve the group consensus problem. The convergence analysis is discussed and the sufficient condition for system group convergence is obtained based on the frequency-domain analysis and generalized Nyquist criterion, respectively. And we know that the condition of group convergence is only depended on system's time delay and the adjacent weight between the agents, meanwhile, delay can affect the dynamic characteristics of the system. Finally, simulations are provided to demonstrate the effectiveness of our theoretical results.

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