Skip to main content
SpringerLink
Log in

Consensus analysis for multiple autonomous agents with input delay and communication delay

  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

Consensus problem is investigated for the multi-agent systems with agents’ dynamics modeled by single-input and single output linear time-invariant proper system, and asynchronously-coupled consensus algorithm is adopted for the system subjected to input delay and communication delay. Sufficient conditions, which depend on the input delay and the communication delay, are obtained for the agents converging to a stationary consensus asymptotically by using linear fractional transformation and small-gain theorem of the frequency-domain analysis. Moreover, the results are extended to get the consensus conditions for second-order multi-agent systems with input delay and communication delay under asynchronously-coupled consensus algorithm, which is composed of the position and the velocity consensus coordination control parts. Simulation illustrates the correctness of the results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Jadbabaie, J. Lin, and A. S. Morse, “Coordination of groups of mobile autonomous agents using nearest neighbor rules,” IEEE Trans. on Automatic Control, vol. 48, no. 6, pp. 988–1001, June 2003.

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  4. L. Moreau, “Stability of multiagent systems with time-dependent communication links,” IEEE Trans. on Automatic Control, vol. 50, no. 2, pp. 169–182, February 2005.

    Article  MathSciNet  Google Scholar 

  5. W. Ren and E. Atkins, “Distributed multi-vehicle coordinated control via local information exchange,” Int. J. Robust Nonlinear Control, vol. 17, no. 10–11, pp. 1002–1033, July 2007.

    Article  MathSciNet  Google Scholar 

  6. Y. Hong, L. Gao, and D. Cheng, et al, “Lyapunov-Based approach to multiagent systems with switching jointly connected interconnection,” IEEE Trans. on Automatic Control, vol. 52, no. 5, pp. 943–948, May 2007.

    Article  MathSciNet  Google Scholar 

  7. J. Zhu, Y.-P. Tian, and J. Kuang, “On the general consensus protocol of multi-agent systems with double-integrator dynamics,” Linear Algebra and its Applications, vol. 431, no. 5–7, pp. 701–715, August 2009.

    Article  MathSciNet  MATH  Google Scholar 

  8. C.-L. Liu and Y.-P. Tian, “Coordination of multiagent systems with communication delays,” Proc. of the 17th IFAC World Congress, pp. 10782–10787, 2008.

  9. P. Lin, Y. Jia, J. Du, and S. Yuan, “Distributed consensus control for second-order agents with fixed topology and time-delay,” Proc. of the 26th Chinese Control Conference, pp. 577–581, 2007.

  10. C.-L. Liu and Y.-P. Tian, “Consensus of multi-agent system with diverse communication delays,” Proc. of the 26th Chinese Control Conference, pp. 726–730, 2007.

  11. W. Yu, G. Chen, and M. Cao, “Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems,” Automatica, vol. 46, no. 6, pp. 1089–1095, June 2010.

    Article  MathSciNet  MATH  Google Scholar 

  12. P. Lin and Y. Jia, “Average consensus in networks of multi-agents with both switching topology and coupling time-delay,” Physica A, vol. 387, no. 1, pp. 303–313, January 2008.

    Article  Google Scholar 

  13. P. Lin, Y. Jia, and L. Li, “Distributed robust H ∞ consensus control in directed networks of agents with time-delay,” System and Control Letters, vol. 57, no. 8, pp. 643–653, August 2008.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. Hu and Y. Hong, “Leader-following coordination of multi-agent systems with coupling time delays,” Physica A, vol. 374, no. 2, pp. 853–863, February 2007.

    Article  Google Scholar 

  15. H. Su and X. Wang, “Second-order consensus of multiple agents with coupling delay,” Proc. of the 7th World Congress on Intelligent Control and Automation, pp. 7181–7186, 2008.

  16. J. Wang and N. Elia, “Consensus over network with dynamic channels,” Proc. of the American Control Conference, pp. 2637–2642, 2008.

  17. L. Moreau, “Stability of continuous-time distributed consensus algorithms,” Proc. of the 43rd IEEE Conference on Decision and Control, pp. 3998–4003, 2004.

  18. W. Wang and J. J. E. Slotine, “Contraction analysis of time-delayed communication delays,” IEEE Trans. on Automatic Control, vol. 51, no. 4, pp. 712–717, April 2006.

    Article  MathSciNet  Google Scholar 

  19. M. Cao, A. S. Morse, and B. D. O. Anderson, “Reaching an agreement using delayed information,” Proc. of the 45th IEEE Conference on Decision and Control, pp. 3375–3380, 2006.

  20. L. Wang and F. Xiao, “A new approach to consensus problems for discrete-time multi-agent systems with time-delays,” Proc. of the American Control Conference, pp. 2118–2123, 2006.

  21. D. J. Lee and M. K. Spong, “Agreement with nonuniform information delays,” Proc. of the American Control Conference, pp. 756–761, 2006.

  22. N. Chopra and M. K. Spong, “Passivity-based control of multi-agent systems,” Advances in Robot Control: From Everyday Physics to Human-Like Movements, Springer-Verlag, New York, pp. 107–134, 2006.

    Google Scholar 

  23. P. Lin and Y. Jia, “Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies,” Automatica, vol. 45, no. 9, pp. 2154–2158, September 2009.

    Article  MathSciNet  MATH  Google Scholar 

  24. W. Yang, A. L. Bertozzi, and X. Wang, “Stability of a second order consensus algorithm with time delay,” Proc. of the 47th IEEE Conference on Decision and Control, pp. 2926–2931, 2008.

  25. U. Munz, A. Papachristodoulou, and F. Allgower, “Delay robustness in consensus problems,” Automatica, vol. 46, no. 8, pp. 1252–1265, 2010.

    Article  MathSciNet  Google Scholar 

  26. Y.-P. Tian and C.-L. Liu, “Consensus of multi-agent systems with diverse input and communication delays,” IEEE Trans. on Automatic Control, vol. 53, no. 9, pp. 2122–2128, September 2008.

    Article  MathSciNet  Google Scholar 

  27. C.-L. Liu and F. Liu, “Consensus problem of second-order dynamic agents with heterogeneous input and communication delays,” Int. J. of Computers, Communications & Control, vol. 5, no. 3, pp. 325–335, September 2010.

    Google Scholar 

  28. Z. Meng, W. Ren, Y. Cao, and Z. You, “Some stability and boundedness conditions for second-order leaderless and leader-following consensus with communication and input delays,” Proc. of the American Control Conference, pp. 574–579, 2010.

  29. Z. Lin, B. Francis, and M. Maggiore, “Necessary and sufficient graphical conditions for formation control of unicycles,” IEEE Trans. on Automatic Control, vol. 50, no. 1, pp. 121–127, January 2005.

    Article  MathSciNet  Google Scholar 

  30. C. A. Desoer and Y. T. Wang, “On the generalized Nyquist stability criterion,” IEEE Trans. on Automatic Control, vol. 25, no. 2, pp. 187–196, April 1980.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute of Automation, Jiangnan University, Wuxi, 214122, China

    Cheng-Lin Liu & Fei Liu

Authors
  1. Cheng-Lin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fei Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cheng-Lin Liu.

Additional information

Recommended by Editorial Board member Guang-Hong Yang under the direction of Editor Zengqi Sun.

This work is supported by the National Natural Science Foundation of China (Grant No. 61104092 and 61134007), the Priority Academic Program Development of Jiangsu Higher Education Institutions and the 111 Project (B12018).

Cheng-Lin Liu received his Ph.D. degree in Control Theory and Control Engineering from Southeast University, China. He is currently an associate professor at Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute of Automation, Jiangnan University, China. His current research interests include Internet congestion control, sensor networks and coordination control of multi-agent systems.

Fei Liu received his Ph.D. degree in Control Science and Control Engineering from Zhejiang University, China. Now he has been a professor of Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute of Automation, Jiangnan University. His research interests include advanced control theory and applications, batch process control engineering, statistical monitoring and diagnosis in industrial process, and intelligent technique with emphasis on fuzzy and neural systems.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, CL., Liu, F. Consensus analysis for multiple autonomous agents with input delay and communication delay. Int. J. Control Autom. Syst. 10, 1005–1012 (2012). https://doi.org/10.1007/s12555-012-0518-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-012-0518-y

Keywords

Search

Navigation