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Leader-following Exponential Consensus of Discrete-time Multi-agent Systems with Time-varying Delay and Intermittent Communication

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Abstract

In this paper, the leader-following exponential consensus problem of discrete-time multi-agent systems with time-varying delay is investigated. For systems with interconnected topology being directed and mobile agents being able to communicate with each other at some disjoint time intervals, a new distributed consensus protocol is proposed. By model transforming, it is shown that the consensus problem can be cast into the stability problem for discrete-time multi-agent systems. In light of the multiple Lyapunov stability analysis and the linear matrix inequality method, some new sufficient conditions are derived for guaranteeing the exponential consensus of discrete-time multi-agent systems under fixed topology and switching topology. Moreover, the corresponding gain matrices are also obtained. Finally, simulation results are provided to illustrate the effectiveness of the theoretical results.

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References

  1. W. J. Sun, “A global asymptotic synchronization problem via internal model approach,” International Journal of Control, Automation, and Systems, vol. 8, no. 5, pp. 1153–1158, October 2010.

    Article  Google Scholar 

  2. J. Yick, B. Mukherjee, and D. Ghosal, “Wireless sensor network survey,” Computer Networks, vol. 52, no. 12, pp. 2292–2330, August 2008.

    Article  Google Scholar 

  3. M. Mauder, “Robust tracking control of nonholonomic dynamic systems with application to the bi-steerable mobile robot,” Automatica, vol. 44, no. 10, pp. 2588–2592, October 2008.

    Article  MathSciNet  Google Scholar 

  4. K. D. Do, “Relative formation control of mobile agents for gradient climbing and target capturing,” International Journal of Control, vol. 84, no. 6, pp. 1098–1114, June 2011.

    Article  MathSciNet  Google Scholar 

  5. R. Olfati-Saber, and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520–1533, September 2004.

    Article  MathSciNet  Google Scholar 

  6. W. Ren and R. W. Beard, “Consensus seeking in multiagent systems under dynamically changing interaction topologies,” IEEE Transactions on Automatic Control, vol. 50, no. 5, pp. 655–661, May 2005.

    Article  MathSciNet  Google Scholar 

  7. Z. X. Liu and Z. Q. Chen, “Discarded consensus of network of agents with state constraint,” IEEE Transactions on Automatic Control, vol. 57, no. 11, pp. 2869–2874, November 2012.

    Article  MathSciNet  Google Scholar 

  8. G. Picci, and T. J. Taylor, “Almost sure exponential convergence to consensus of random gossip algorithms,” International Journal of Robust and Nonlinear Control, vol. 23, no. 9, pp. 1033–1045, June 2013.

    Article  MathSciNet  Google Scholar 

  9. Y. Tanga, H. J. Gao, W. B. Zhang, and J. Kurths, “Leader-following consensus of a class of stochastic delayed multiagent systems with partial mixed impulses,” Automatica, vol. 53, pp. 346–354, March 2015.

    Article  MathSciNet  Google Scholar 

  10. Z. Y. Meng, Z. Y. Zhao, and Z. L. Lin, “On global leader-following consensus of identical linear dynamic systems subject to actuator saturation,” Systems & Control Letters, vol. 62, no. 2, pp. 132–142, February 2013.

    Article  MathSciNet  Google Scholar 

  11. W. L. Guo, “Leader-following consensus of the second-order multi-agent systems under directed topology,” ISA Transactions, vol. 65, pp. 116–124, November 2016.

    Article  Google Scholar 

  12. Z. K. Li, W. Ren, X. D. Liu, and M. Y. Fu, “Distributed containment control of multi-agent systems with general linear dynamics in the presence of multiple leaders,” International Journal of Robust and Nonlinear Control, vol. 23, no. 5, pp. 534–547, March 2013.

    Article  MathSciNet  Google Scholar 

  13. Z. Yang, X. W. Mu, and K. Liu, “Containment control of continuous-time multi-agent systems with general linear dynamics under time-varying communication topologies,” International Journal of Control, Automation and Systems, vol. 15, no. 1, pp. 442–449, February 2017.

    Article  Google Scholar 

  14. F. Y. Wang, Y. H. Ni, Z. X. Liu, and Z. Q. Chen, “Containment control for general second-order multiagent systems with switched dynamics,” IEEE Transactions on Cybernetics, 2018. DOI: 10.1109/TCYB.2018.2869706

    Google Scholar 

  15. Z. Wang, J. X. Xi, Z. Y. Yu, and G. B. Liu, “Guaranteed cost consensus for multi-agent systems with time delays,” Journal of the Franklin Institute, vol. 352, no. 9, pp. 3612–3627, September 2015.

    Article  MathSciNet  Google Scholar 

  16. H. Y. Hu and Z. L. Lin, “Consensus of a class of discrete-time nonlinear multi-agent systems in the presence of communication delays,” ISA Transactions, vol. 71, pp. 10–20, November 2017.

    Article  Google Scholar 

  17. J. P. Zhou, C. Y. Sang, X. Li, M. Y. Fang, and Z. Wang, “H∞ consensus for nonlinear stochastic multi-agent systems with time delay,” Applied Mathematics and Computation, vol. 325, pp. 41–58, May 2018.

    Article  MathSciNet  Google Scholar 

  18. G. H. Wen, Z. S. Duan, W. Ren, and G. R. Chen, “Distributed consensus of multi-agent systems with general linear node dynamics and intermittent communications,” International Journal of Robust and Nonlinear Control, vol. 24, no. 16, pp. 2438–2457, November 2014.

    Article  MathSciNet  Google Scholar 

  19. W. Qin, Z. X. Liu, and Z. Q. Chen, “Observer-based consensus for nonlinear multi-agent systems with intermittent communication,” Neurocomputing, vol. 154, pp. 230–238, April 2015.

    Article  Google Scholar 

  20. N. Huang, Z. S. Duan, and Y. Zhao, “Leader-following consensus of second-order non-linear multi-agent systems with directed intermittent communication,” IET Control Theory and Applications, vol. 8, no. 10, pp. 782–795, July 2014.

    Article  MathSciNet  Google Scholar 

  21. L. Liu and J. J. Shan, “Event-triggered consensus of nonlinear multi-agent systems with stochastic switching topology,” Journal of the Franklin Institute, vol. 354, no. 13, pp. 5350–5373, September 2017.

    Article  MathSciNet  Google Scholar 

  22. Y. H. Ji, H. L. Zhou, and Q. Gao, “Distributed containment control for multi-agent systems in pure-feedback form under switching topologies,” International Journal of Control, Automation and Systems, vol. 16, no. 5, pp. 2312–2320, October 2018.

    Article  Google Scholar 

  23. J. H. Qin and C. B. Yu, “Exponential consensus of general linear multi-agent systems under directed dynamic topology,” Automatica, vol. 50, no. 9, pp. 2327–2333, September 2014.

    Article  MathSciNet  Google Scholar 

  24. R. Sakthivel, R. Sakthivel, B. Kaviarasan, and F. Alzahrani, “Leader-following exponential consensus of input saturated stochastic multi-agent systems with Markov jump parameters,” Neurocomputing, vol. 287, pp. 84–92, April 2018.

    Article  Google Scholar 

  25. Y. Y. Wang, L. H. Xie, and C. E. Souza, “Robust control of a class of uncertain nonlinear systems,” Systems & Control Letters, vol. 19, no. 2, pp. 139–149, August 1992.

    Article  MathSciNet  Google Scholar 

  26. E. Semsar-Kazerooni and K. Khorasani, “Switching control of a modified leader-follower team of agents under the leader and network topological changes,” IET Control Theory and Applications, vol. 5, no. 12, pp. 1369–1377, August 2011.

    Article  MathSciNet  Google Scholar 

  27. X. M. Zhang and Q. L. Han, “Abel lemma-based finite-sum inequality and its application to stability analysis for linear discrete time-delay systems,” Automatica, vol. 57, pp. 199–202, July 2015.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. College of Artificial Intelligence, Nankai University, Tianjin, 300350, China

    Shuang Liang, Zhongxin Liu & Zengqiang Chen

  2. Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin, 300350, China

    Shuang Liang, Zhongxin Liu & Zengqiang Chen

Authors
  1. Shuang Liang
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  2. Zhongxin Liu
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  3. Zengqiang Chen
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Correspondence to Zhongxin Liu.

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Recommended by Associate Editor Sung Jin Yoo under the direction of Editor Jessie (Ju H.) Park. This work was supported by the National Natural Science Foundation of China (Grant No.61573200,61573199).

Shuang Liang received her M.S. degree from the School of Tianjin Polytechnic University, Tianjin, China, in 2017. She is now pursuing a Ph.D. degree in the College of Artificial Intelligence, Nankai University, Tianjin, China. Her research interest covers complex networks and consensus of multi-agent systems.

Zhongxin Liu received his B.S. degree in automation and Ph.D. degree in control theory and control engineering from the Nankai University, Tianjin, China, in 1997 and 2002, respectively. He has been at Nankai University, where he is currently a Professor in the Department of Automation. His main areas of research are in predictive control, complex networks and multi-agent systems.

Zengqiang Chen received his B.S. degree in mathematics, M.S. degree and a Ph.D. degree in control theory from Nankai University, China, in 1987, 1990, and 1997, respectively. He is now a professor at the College of Artificial Intelligence, Nankai University. His research interest covers complex networks, adaptive control, intelligent predictive control and chaos system.

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Liang, S., Liu, Z. & Chen, Z. Leader-following Exponential Consensus of Discrete-time Multi-agent Systems with Time-varying Delay and Intermittent Communication. Int. J. Control Autom. Syst. 18, 944–954 (2020). https://doi.org/10.1007/s12555-019-0366-0

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  • DOI: https://doi.org/10.1007/s12555-019-0366-0

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