Skip to main content
SpringerLink
Log in

A Class of Second-Order Consensus Protocol in Multi-Agent Systems with Multiple Input Delays

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

This paper is concerned with the consensus problems for second-order multi-agent systems with multiple input delays. Different from all standard consensus algorithms with uniform delays, the authors aim to find the largest input-delay margin which can guarantee the consensus for the case when delays are nonuniform. Based on frequency domain analysis and matrix theory, an upper bound for maximum tolerable input-delay is given in terms of the relationship with scaling strengths and largest eigenvalue of the Lapalician matrix. Simulation results are provided to illustrate the obtained 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. Chen F, Chen Z Q, Xiang L Y, et al., Reaching a consensus via pinning control, Automatica, 2009, 45(5): 1215–1220.

    Article  MathSciNet  Google Scholar 

  2. Silva Pereira S and Pages-Zamora A, Consensus in correlated random wireless sensor networks, IEEE Trans. Signal Processing, 2011, 59(12): 6279–6284.

    Article  MathSciNet  Google Scholar 

  3. Fax J A and Murray R M, Information flow and cooperative control of vehicle formation, IEEE Trans. Automatic Control, 2004, 49(9): 1465–1476.

    Article  MathSciNet  Google Scholar 

  4. Olfatisaber R, Flocking for multi-agent dynamic systems: Algorithms and theory, IEEE Trans. Automatic Control, 2006, 51(3): 401–420.

    Article  MathSciNet  Google Scholar 

  5. Dimarogonas D V and Kyriakopoulos K J, On the rendezvous problem for multiple nonholonomic agents, IEEE Trans. Automatic Control, 2007, 52(5): 916–922.

    Article  MathSciNet  Google Scholar 

  6. Olfatisaber R and Murray R M, Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Automatic Control, 2004, 49(9): 1520–1533.

    Article  MathSciNet  Google Scholar 

  7. Ren W and Beard R W, Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE Trans. Automatic Control, 2005, 50(5): 655–661.

    Article  MathSciNet  Google Scholar 

  8. Ren W and Atkins E, Distributed multi-vehicle coordinated control via local information exchange, Int. J. Robust Nonlinear Control, 2007, 17: 1002–1033.

    Article  MathSciNet  Google Scholar 

  9. Lin P, Jia Y M, Du J P, et al., Distributed consensus control for second-order agents with fixed topology and time-delay, Proceedings of the 26th Chinese Control Conference, Zhangjiajie, Hunan, 2007.

    Google Scholar 

  10. Tian Y P and Liu C L, Consensus of multi-agent systems with diverse input and communication delays, IEEE Trans. Automatic Control, 2008, 53(9): 2122–2128.

    Article  MathSciNet  Google Scholar 

  11. Lin P and Jia Y M, Consensus of a class of second-order multi-agent systems with time-delay and jointly-connected topologies, IEEE Trans. Automatic Control, 2010, 55(3): 778–784.

    Article  MathSciNet  Google Scholar 

  12. Xu J J, Zhang H S, and Xie L H, Input delay margin for consensusability of multi-agent systems, Automatica, 2013, 49(6): 1816–1820.

    Article  MathSciNet  Google Scholar 

  13. Hou W Y, Fu M Y, Zhang H S, et al., Consensus conditions for general second-order multi-agent systems with communication delay, Automatica, 2017, 75: 293–298.

    Article  MathSciNet  Google Scholar 

  14. Liu C L and Liu F, Consensus of second-order multi-agent systems with input delay, Proceedings of the 22nd Chinese Control and Decision Conference, Xuzhou, 2010.

    Google Scholar 

  15. Lin P, Dai M X, and Song Y D, Consensus stability of a class of second-order multi-agent systems with nonuniform time-delays, Journal of the Franklin Institute, 2014, 351(3): 1571–1576.

    Article  MathSciNet  Google Scholar 

  16. Li X, Gao K, Lin P, et al., A futher result on consensus problems of second-order multi-agent systems with directed graphs, a moving mode and multiple delays, ISA Transactions, 2017, 71(1): 21–24.

    Article  Google Scholar 

  17. Godsil C and Royle G, Algebraic Graph Theory, Springer-Verlag, New York, 2001.

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Application, China Academy of Engineering Physics, Mianyang, 621900, China

    Huai Wu & Baoran An

  2. Jiangsu Automation Research Institute, Lianyungang, 222061, China

    Kai Gao

Authors
  1. Huai Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kai Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Baoran An
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Baoran An.

Additional information

This research was supported by the Defense Industrial Development Program of China under Grant No. JCKY2017212C005.

This paper was recommended for publication by Editor LIU Guoping.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, H., Gao, K. & An, B. A Class of Second-Order Consensus Protocol in Multi-Agent Systems with Multiple Input Delays. J Syst Sci Complex 32, 1280–1289 (2019). https://doi.org/10.1007/s11424-018-7441-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-018-7441-0

Keywords

Search

Navigation