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

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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.

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References

  1. Shang Y. Fast distributed consensus seeking in large-scale sensor networks via shortcuts. Int J Comput Scien Engin, 2012, 7: 121–124

    Article  Google Scholar 

  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: 427–438

    Article  Google Scholar 

  3. Ugrinovskii V. Distributed robust filtering with consensus of estimates. Automatica, 2011, 47: 1–13

    Article  MathSciNet  MATH  Google Scholar 

  4. Ren W, Beard R W. Consensus seeking in multi-agent systems under dynamically changing interaction topologies. IEEE Trans Autom Contr, 2005, 50: 655–661

    Article  Google Scholar 

  5. Ma C Q, Zhang J F. Necessary and sufficient conditions for consensusability of linear multi-agent systems. IEEE Trans Autom Contr, 2010, 55: 1263–1268

    Article  MathSciNet  Google Scholar 

  6. Wang L, Liu Z X. Robust consensus of multi-agent systems with noise. Sci China Inf Sci, 2009, 52: 824–834

    Article  MathSciNet  MATH  Google Scholar 

  7. Hale J K, Lunel S M V. Introduction to Functional Difference Equations. New York: Springer-Verlag,1993

    Book  MATH  Google Scholar 

  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: 1520–1533

    Article  MathSciNet  Google Scholar 

  9. Huang M Y. Stochastic approximation for consensus: a new approach via ergodic backward products. IEEE Trans Autom Contr, 2012, 57: 2994–3008

    Article  MathSciNet  Google Scholar 

  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: 920–934

    Article  MathSciNet  MATH  Google Scholar 

  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: 2239–2262

    Article  MATH  Google Scholar 

  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: 1235–1241

    Article  MathSciNet  MATH  Google Scholar 

  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: 153–158

    Article  Google Scholar 

  14. Wang X, Saberi A, Stoovogel A A, et al. Consensus in network with uniform constant communication delay. Automatica, 2013, 49: 2461–2467

    Article  MathSciNet  Google Scholar 

  15. Zhou B, Lin Z L. Consensus of high-order multi-agent systems with large input and communication delays. Automatica, 2014, 50: 452–464

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  17. Tian Y P, Zhang Y. High-order consensus of heterogeneous multi-agent systems with unknown communication delay. Automatica, 2012, 48: 1205–1212

    Article  MathSciNet  MATH  Google Scholar 

  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: 2172–2181

    Article  MathSciNet  MATH  Google Scholar 

  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: 2529–2541

    Article  MathSciNet  MATH  Google Scholar 

  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: 837–844

    Article  MathSciNet  MATH  Google Scholar 

  21. Lin Z L, Fang H J. On asymptotic stabilizability of linear systems with delayed input. IEEE Trans Autom Contr, 2007, 52: 998–1013

    Article  MathSciNet  Google Scholar 

  22. Horn R A, Johnson C R. Topics in Matrix Analysis. Cambrige: Cambrige University Press,1991

    Book  MATH  Google Scholar 

  23. Fiedler F. Laplacian matrices of graph: a survey. Linear Algebra Appl, 1994, 197: 143–176

    MathSciNet  Google Scholar 

  24. Barahona M, Pecora L M. Synchronization in small-world systems. Phys Rev Lett, 2002, 89: 054101

    Article  Google Scholar 

  25. Lin P, Ren W, Song Y D. Distributed multi-agent optimization subject to nonidentical constraints and communication delays. Automatica, 2016, 65: 120–131

    Article  MathSciNet  MATH  Google Scholar 

  26. Artstein Z. Linear systems with delayed controls: a reduction. IEEE Trans Autom Contr, 1982, 27: 869–879

    Article  MathSciNet  MATH  Google Scholar 

  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: 2730–2738

    Article  MathSciNet  Google Scholar 

  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: 1548–1554

    Article  MathSciNet  Google Scholar 

  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. 2805–2810

    Google Scholar 

  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: 37–42

    Article  MathSciNet  MATH  Google Scholar 

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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).

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Authors and Affiliations

  1. School of Information Science and Engineering, Shandong Normal University, Jinan, 250014, China

    Zhenhua Wang & Huaxiang Zhang

  2. Institute of Data Science and Technology, Shandong Normal University, Jinan, 250014, China

    Zhenhua Wang & Huaxiang Zhang

  3. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Huanshui Zhang

  4. School of Electrical Engineering and Computer Science, University of Newcastle, Callaghan, NSW, 2308, Australia

    Minyue Fu

  5. School of Automation, Guangdong Key Laboratory of IoT Information Technology, Guangdong University of Technology, Guangzhou, 510006, China

    Minyue Fu

Authors
  1. Zhenhua Wang
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  2. Huanshui Zhang
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  3. Minyue Fu
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  4. Huaxiang Zhang
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Correspondence to Zhenhua Wang.

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Wang, Z., Zhang, H., Fu, M. et al. Consensus for high-order multi-agent systems with communication delay. Sci. China Inf. Sci. 60, 092204 (2017). https://doi.org/10.1007/s11432-016-0094-7

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  • DOI: https://doi.org/10.1007/s11432-016-0094-7

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