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Science China Information Sciences

, 60:092204 | Cite as

Consensus for high-order multi-agent systems with communication delay

  • Zhenhua WangEmail author
  • Huanshui Zhang
  • Minyue Fu
  • Huaxiang Zhang
Research Paper

Abstract

In this study, consensus problem for general high-order multi-agent systems with communication delay is investigated. Given the unstable agent dynamics and a known communication delay, two consensus protocols are designed to guarantee consensus over undirected network. By jointly researching the effects of agent dynamics and network topology, allowable delay bounds depending on the maxima of concave functions are easy to calculate. Especially, the maximum delay bound is derived when the network topology is completely connected. The main approach for the same involves designing the control gains on the basis of the solution of a parametric algebraic Riccati equation. Finally, the theoretical results are demonstrated via numerical simulations.

Keywords

consensus communication delay historical input information parametric algebraic Riccati equation eigenratio 

Notes

Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant Nos. 61120106011, 61403235, 61573221, 61633014) and Natural Science Foundation of Shandong Province (Grant Nos. ZR2014FQ011, BS2015DX016).

References

  1. 1.
    Shang Y. Fast distributed consensus seeking in large-scale sensor networks via shortcuts. Int J Comput Scien Engin, 2012, 7: 121–124CrossRefGoogle Scholar
  2. 2.
    Cao Y, Yu W W, Ren W, et al. An overview of recent progress in the study of distributed multi-agent coordination. IEEE Trans Ind Inform, 2013, 9: 427–438CrossRefGoogle Scholar
  3. 3.
    Ugrinovskii V. Distributed robust filtering with consensus of estimates. Automatica, 2011, 47: 1–13MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Ren W, Beard R W. Consensus seeking in multi-agent systems under dynamically changing interaction topologies. IEEE Trans Autom Contr, 2005, 50: 655–661CrossRefGoogle Scholar
  5. 5.
    Ma C Q, Zhang J F. Necessary and sufficient conditions for consensusability of linear multi-agent systems. IEEE Trans Autom Contr, 2010, 55: 1263–1268MathSciNetCrossRefGoogle Scholar
  6. 6.
    Wang L, Liu Z X. Robust consensus of multi-agent systems with noise. Sci China Inf Sci, 2009, 52: 824–834MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Hale J K, Lunel S M V. Introduction to Functional Difference Equations. New York: Springer-Verlag,1993CrossRefzbMATHGoogle Scholar
  8. 8.
    Olfati-Saber R, Murray R M. Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Contr, 2004, 49: 1520–1533MathSciNetCrossRefGoogle Scholar
  9. 9.
    Huang M Y. Stochastic approximation for consensus: a new approach via ergodic backward products. IEEE Trans Autom Contr, 2012, 57: 2994–3008MathSciNetCrossRefGoogle Scholar
  10. 10.
    Liu S, Xie L H, Zhang H S. Distributed consensus for multi-agent systems with delays and noises in transmission channels. Automatica, 2011, 47: 920–934MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Liu S, Li T, Xie L H. Distributed consensus for multi-agent systems with communication delays and limited data rate. SIAM J Contr Optim, 2011, 49: 2239–2262CrossRefzbMATHGoogle Scholar
  12. 12.
    Liu C L, Liu F. Dynamical consensus seeking of second-order multi-agent systems based on delayed state compensation. Syst Contr Lett, 2012, 61: 1235–1241MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Savino H J, Souza F O, Pimetnta L C A. Consensus on time-delay intervals in networks of high-order integrator agents. IFAC-Papers Online, 2015, 48: 153–158CrossRefGoogle Scholar
  14. 14.
    Wang X, Saberi A, Stoovogel A A, et al. Consensus in network with uniform constant communication delay. Automatica, 2013, 49: 2461–2467MathSciNetCrossRefGoogle Scholar
  15. 15.
    Zhou B, Lin Z L. Consensus of high-order multi-agent systems with large input and communication delays. Automatica, 2014, 50: 452–464MathSciNetCrossRefGoogle Scholar
  16. 16.
    Xu J J, Zhang H S, Xie L H. Input delay margin for consensusability of multi-agent systems. Automatica, 2013, 49: 1816–1820MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Tian Y P, Zhang Y. High-order consensus of heterogeneous multi-agent systems with unknown communication delay. Automatica, 2012, 48: 1205–1212MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Zhang Y, Tian Y P. Allowable delay bound for consensus of linear multi-agent systems with communication delay. Inter J Syst Sci, 2014, 45: 2172–2181MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Hou W Y, Fu M Y, Zhang H S. Consensusability of linear multi-agent systems with time-delay. Int J Robust Nonlin Contr, 2016, 26: 2529–2541MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Yoon S Y, Lin Z L. Truncated predictor feedback control for exponentially unstable linear systems with time-varying input delay. Syst Contr Lett, 2013, 62: 837–844MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Lin Z L, Fang H J. On asymptotic stabilizability of linear systems with delayed input. IEEE Trans Autom Contr, 2007, 52: 998–1013MathSciNetCrossRefGoogle Scholar
  22. 22.
    Horn R A, Johnson C R. Topics in Matrix Analysis. Cambrige: Cambrige University Press,1991CrossRefzbMATHGoogle Scholar
  23. 23.
    Fiedler F. Laplacian matrices of graph: a survey. Linear Algebra Appl, 1994, 197: 143–176MathSciNetGoogle Scholar
  24. 24.
    Barahona M, Pecora L M. Synchronization in small-world systems. Phys Rev Lett, 2002, 89: 054101CrossRefGoogle Scholar
  25. 25.
    Lin P, Ren W, Song Y D. Distributed multi-agent optimization subject to nonidentical constraints and communication delays. Automatica, 2016, 65: 120–131MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Artstein Z. Linear systems with delayed controls: a reduction. IEEE Trans Autom Contr, 1982, 27: 869–879MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Wang C Y, Zuo Z Y, Lin Z L, et al. Consensus control of a class of Lipschitz nonlinear systems with input delay. IEEE Trans Circuits Syst I-Reg Papers, 2015, 62: 2730–2738MathSciNetCrossRefGoogle Scholar
  28. 28.
    Zhou B, Duan G R, Lin Z L. A parametric lyapunov equation approach to the design of low gain feedback. IEEE Trans Autom Contr, 2008, 53: 1548–1554MathSciNetCrossRefGoogle Scholar
  29. 29.
    Gu K Q. An integral inequality in the stability problem of time-delay systems. In: Proceedings of the 39th IEEE Conference on Service Operations and Logistics, and Control, Sydney, 2000. 2805–2810Google Scholar
  30. 30.
    Wang Z H, Xu J J, Zhang H S. Consensusability of multi-agent systems with time-varying communication delay. Syst Contr Lett, 2014, 65: 37–42MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Zhenhua Wang
    • 1
    • 2
    Email author
  • Huanshui Zhang
    • 3
  • Minyue Fu
    • 4
    • 5
  • Huaxiang Zhang
    • 1
    • 2
  1. 1.School of Information Science and EngineeringShandong Normal UniversityJinanChina
  2. 2.Institute of Data Science and TechnologyShandong Normal UniversityJinanChina
  3. 3.School of Control Science and EngineeringShandong UniversityJinanChina
  4. 4.School of Electrical Engineering and Computer ScienceUniversity of NewcastleCallaghanAustralia
  5. 5.School of Automation, Guangdong Key Laboratory of IoT Information TechnologyGuangdong University of TechnologyGuangzhouChina

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