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Consensus problems of first-order and second-order multi-agent system with communication delays and input delays are proposed based on the frequency-domain analysis and generalized Nyquist criterion. Supposing that the topology of the multi-agent system is fixed, asymmetrically interconnected digraph and owns a globally reachable node, the sufficient condition for system convergence is obtained. The results show that the condition of convergence is dependent only on system coupling strength, each agent input time delay and the adjacent weights to its neighbors, but independent of communication delay which can affect the dynamics of the system. Finally, simulations are provided to demonstrate the effectiveness of our theoretical results.
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Keywords:
- multi-agent /
- time delay /
- consensus /
- convergence
[1] Yu W W, Chen G R, Wang Z D, Yang W 2009 IEEE Trans. on Syst. Man Cybern. 39 1568
[2] Paganini F, Doyle J, Low S 2001 Proceedings of the International Conference on Decision and Control Orlando, Florida, USA, December 4-7, 2001 p185
[3] Olfati-Saber R 2006 IEEE Trans. on Autom. Control 51 401
[4] Liu T L, Huang H J 2007 Acta Phys. Sin. 56 6321 (in Chinese) [刘天亮, 黄海军 2007 物理学报 56 6321]
[5] Li Y M, Guan X P 2009 Chin. Phys. B 18 3355
[6] Hu J P, Yuan H W 2009 Chin. Phys. B 18 3777
[7] Tan F X, Guan X P, Liu D R 2008 Chin. Phys. B 17 3531
[8] Sun Y Z, Ruan J 2008 Chin. Phys. B 17 4137
[9] Bliman P A, Ferrari-Trecate G 2008 Automatica 44 1985
[10] Liu C L, Tian Y P 2009 Control and Decision 24 1601 (in Chinese) [刘成林, 田玉平 2009 控制与决策 24 1601]
[11] Vicsek T, Czirok A, Ben-Jacob E 1995 Phys. Rev. Lett. 75 1226
[12] Jadbabaie A, Lin J, Morse A S 2003 IEEE Trans. on Autom. Control 48 988
[13] Olfati-Saber R, Murray R M 2004 IEEE Trans. on Autom. Control 49 1520
[14] Ren W, Beard R W 2005 IEEE Trans. on Autom. Control 50 655
[15] Moreau L 2005 IEEE Trans. on Autom. Control 50 169
[16] Yu H, Jian J G, Wang Y J 2007 Control and Decision 22 558(in Chinese) [俞辉, 蹇继贵, 王永骥 2007 控制与决策 22 558]
[17] Yang H Y, Zhang S Y 2009 Control and Decision 24 413 (in Chinese) [杨洪勇, 张嗣瀛 2009 控制与决策 24 413]
[18] Tian Y P, Liu C L 2008 IEEE Trans. on Autom. Control 53 2122
[19] Wang W, Slotine J J E 2006 IEEE Trans. on Autom. Control 51 712
[20] Yang W, Bertozzi A L, Wang X F 2008 Proceedings of the 47th IEEE Conference on Decision and Control Cancun, Mexico, December 9-11, 2008 p2926
[21] Lin P, Jia Y M, Du J P 2008 American Control Conference Seattle, Washington, June 11-13, 2008 p1564
[22] Tian Y P, Liu C L 2009 Automatica 45 1347
[23] Li H, Lin P, Zhang C X 2009 Acta Phys. Sin. 58 158 (in Chinese) [李慧, 林鹏, 张春熹 2009 物理学报 58 158]
[24] Lin P, Jia Y M 2010 IEEE Trans. on Autom. Control 55 778
[25] Liu C L, Liu F 2011 Acta Phys. Sin. 60 030202 (in Chinese) [刘成林, 刘飞 2011 物理学报 60 030202]
[26] Liu C L, Tian Y P 2008 Journal of Southeast University (Natural Science Edition) 38 170 (in Chinese) [刘成林, 田玉平 2008 东南大学学报(自然科学版) 38 170]
[27] Tian Y, Yang H 2004 Proceedings of the 5th World Congress on Intelligent Control and Automation Hangzhou, China, June 14-15, 2004 p15
[28] 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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[1] Yu W W, Chen G R, Wang Z D, Yang W 2009 IEEE Trans. on Syst. Man Cybern. 39 1568
[2] Paganini F, Doyle J, Low S 2001 Proceedings of the International Conference on Decision and Control Orlando, Florida, USA, December 4-7, 2001 p185
[3] Olfati-Saber R 2006 IEEE Trans. on Autom. Control 51 401
[4] Liu T L, Huang H J 2007 Acta Phys. Sin. 56 6321 (in Chinese) [刘天亮, 黄海军 2007 物理学报 56 6321]
[5] Li Y M, Guan X P 2009 Chin. Phys. B 18 3355
[6] Hu J P, Yuan H W 2009 Chin. Phys. B 18 3777
[7] Tan F X, Guan X P, Liu D R 2008 Chin. Phys. B 17 3531
[8] Sun Y Z, Ruan J 2008 Chin. Phys. B 17 4137
[9] Bliman P A, Ferrari-Trecate G 2008 Automatica 44 1985
[10] Liu C L, Tian Y P 2009 Control and Decision 24 1601 (in Chinese) [刘成林, 田玉平 2009 控制与决策 24 1601]
[11] Vicsek T, Czirok A, Ben-Jacob E 1995 Phys. Rev. Lett. 75 1226
[12] Jadbabaie A, Lin J, Morse A S 2003 IEEE Trans. on Autom. Control 48 988
[13] Olfati-Saber R, Murray R M 2004 IEEE Trans. on Autom. Control 49 1520
[14] Ren W, Beard R W 2005 IEEE Trans. on Autom. Control 50 655
[15] Moreau L 2005 IEEE Trans. on Autom. Control 50 169
[16] Yu H, Jian J G, Wang Y J 2007 Control and Decision 22 558(in Chinese) [俞辉, 蹇继贵, 王永骥 2007 控制与决策 22 558]
[17] Yang H Y, Zhang S Y 2009 Control and Decision 24 413 (in Chinese) [杨洪勇, 张嗣瀛 2009 控制与决策 24 413]
[18] Tian Y P, Liu C L 2008 IEEE Trans. on Autom. Control 53 2122
[19] Wang W, Slotine J J E 2006 IEEE Trans. on Autom. Control 51 712
[20] Yang W, Bertozzi A L, Wang X F 2008 Proceedings of the 47th IEEE Conference on Decision and Control Cancun, Mexico, December 9-11, 2008 p2926
[21] Lin P, Jia Y M, Du J P 2008 American Control Conference Seattle, Washington, June 11-13, 2008 p1564
[22] Tian Y P, Liu C L 2009 Automatica 45 1347
[23] Li H, Lin P, Zhang C X 2009 Acta Phys. Sin. 58 158 (in Chinese) [李慧, 林鹏, 张春熹 2009 物理学报 58 158]
[24] Lin P, Jia Y M 2010 IEEE Trans. on Autom. Control 55 778
[25] Liu C L, Liu F 2011 Acta Phys. Sin. 60 030202 (in Chinese) [刘成林, 刘飞 2011 物理学报 60 030202]
[26] Liu C L, Tian Y P 2008 Journal of Southeast University (Natural Science Edition) 38 170 (in Chinese) [刘成林, 田玉平 2008 东南大学学报(自然科学版) 38 170]
[27] Tian Y, Yang H 2004 Proceedings of the 5th World Congress on Intelligent Control and Automation Hangzhou, China, June 14-15, 2004 p15
[28] 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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