Skip to main content
SpringerLink
Log in

Event-based consensus control of Lipschitz nonlinear multi-agent systems with unknown input delay and quantization constraints

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

This paper deals with an event-triggered protocol design for achieving global exponential consensus of Lipschitz nonlinear multi-agent systems (MASs) with unknown time-varying input delay and state quantization constraints. For such MASs, an event-triggered delay independent truncated predictor feedback (ET-DITPF) protocol is designed using the information of the upper bound of time-varying input delay (and not its exact value). A sufficient condition on the upper bound value of time-varying input delay is established under which the global consensus of the MASs in the presence of the state quantization constraints is achieved. Also, the avoidance of Zeno behavior is proved by finding a lower bound for each two successive events. A simulation study confirms the effectiveness of 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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. K.K. Oh, M.C. Park, H.S. Ahn, A survey of multi-agent formation control. Automatica 53, 424–440 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  2. Y. Cao, W. Yu, W. Ren, G. Chen, An overview of recent progress in the study of distributed multi-agent coordination. IEEE Trans. Ind. Inform. 9(1), 427–438 (2012)

    Article  Google Scholar 

  3. J. Qin, Q. Ma, Y. Shi, L. Wang, Recent advances in consensus of multi-agent systems: a brief survey. IEEE Trans. Ind. Electron. 64(6), 4972–4983 (2016)

    Article  Google Scholar 

  4. L. Shi, W. Guo, W. He, Distributed adaptive discontinuous consensus tracking control for disturbed multi-agent systems based on input-observers. Eur. Phys. J. Spec. Top., 1–8 (2022)

  5. G. Wen, Z. Duan, G. Chen, W. Yu, Consensus tracking of multi-agent systems with lipschitz-type node dynamics and switching topologies. IEEE Trans. Circuits Syst. I Regul. Pap. 61(2), 499–511 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. L. Xing, C. Wen, H. Su, Z. Liu, J. Cai, Robust control for a class of uncertain nonlinear systems with input quantization. Int. J. Robust Nonlinear Control 26(8), 1585–1596 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  7. Z. Zhang, L. Zhang, F. Hao, L. Wang, Leader-following consensus for linear and Lipchitz nonlinear multiagent systems with quantized communication. IEEE Trans. Cybern. 47(8), 1970–1982 (2016)

    Article  Google Scholar 

  8. J. Zhang, S. Liu, X. Zhang, Output-feedback distributed consensus for nonlinear multi-agent systems with quantization. Inform. Sci. 585, 246–261 (2022)

    Article  Google Scholar 

  9. S. Feng, H. Ishii, Dynamic quantized consensus of general linear multi-agent systems under denial-of-service attacks. IEEE Trans. Control Netw. Syst. (2022). https://doi.org/10.1109/TCNS.2022.3140684

    Article  Google Scholar 

  10. S. Xiong, Q. Wu, Y. Wang, Distributed coordination of heterogeneous multi-agent systems with dynamic quantization and \(\cal{L}_2\)-\(\cal{L}_\infty\) control. Int. J. Control Autom. Syst. 18(10), 2468–2481 (2020)

    Article  Google Scholar 

  11. L. Ding, Q.L. Han, X. Ge, X.M. Zhang, An overview of recent advances in event-triggered consensus of multiagent systems. IEEE Trans. Cybern. 48(4), 1110–1123 (2017)

    Article  Google Scholar 

  12. Z.G. Wu, Y. Xu, Y.J. Pan, H. Su, Y. Tang, Event-triggered control for consensus problem in multi-agent systems with quantized relative state measurements and external disturbance. IEEE Trans. Circuits Syst. I Regul. Pap. 65(7), 2232–2242 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Ma, L. Liu, H. Ji, G. Feng, Quantized consensus of multiagent systems by event-triggered control. IEEE Trans. Syst. Man Cybern. Syst. 50(9), 3231–3242 (2018)

    Article  Google Scholar 

  14. N. Lin, Q. Ling, Bit-rate conditions for the consensus of quantized multiagent systems based on event triggering. IEEE Trans. Cybern. 52(1), 116–127 (2022)

    Article  Google Scholar 

  15. K. Li, Q. Liu, Z. Zeng, Quantized event-triggered communication based multi-agent system for distributed resource allocation optimization. Inform. Sci. 577, 336–352 (2021)

    Article  MathSciNet  Google Scholar 

  16. C. Wang, Z. Zuo, Z. Lin, Z. Ding, A truncated prediction approach to consensus control of Lipchitz nonlinear multiagent systems with input delay. IEEE Trans. Control Netw. Syst. 4(4), 716–724 (2016)

    Article  MATH  Google Scholar 

  17. Y. Li, C. Wang, D. Liang, Truncated prediction-based distributed consensus control of linear multi-agent systems with discontinuous communication and input delay. Neurocomputing 409, 217–230 (2020)

    Article  Google Scholar 

  18. H. Chu, L. Gao, D. Yue, C. Dou, Consensus of Lipchitz nonlinear multiagent systems with input delay via observer-based truncated prediction feedback. IEEE Trans. Syst. Man Cybern. Syst. 50(10), 3784–3794 (2019)

    Google Scholar 

  19. H. Chu, D. Yue, C. Dou, X. Xie, L. Chu, Consensus of multiagent systems with time-varying input delay via truncated predictor feedback. IEEE Trans. Syst. Man Cybern. Syst. 51(10), 6062–6073 (2019)

    Article  Google Scholar 

  20. B. Zhou, Z. Lin, Consensus of high-order multi-agent systems with large input and communication delays. Automatica 50(2), 452–464 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  21. N. Lin, Q. Ling, An event-triggered consensus protocol for quantized second-order multi-agent systems with network delay and process noise. ISA Trans. (2021). https://doi.org/10.1016/j.isatra.2021.06.026

    Article  Google Scholar 

  22. M.Z. Dai, F. Xiao, B. Wei, Event-triggered and quantized self-triggered control for multi-agent systems based on relative state measurements. J. Franklin Inst. 356(6), 3711–3732 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  23. M. Yu, C. Yan, D. Xie, Event-triggered control for couple-group multi-agent systems with logarithmic quantizers and communication delays. Asian J. Control 19(2), 681–691 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  24. Y. Xie, Y. Wei, Z. Lin, Stabilization of linear systems with input delay by event-triggered delay independent truncated predictor feedback. 2019 American Control Conference (ACC) pp. 3708–3713 (2019)

  25. Y. Xie, Y. Wei, Z. Lin, Stabilization of linear systems with time-varying input delay by event-triggered delay independent truncated predictor feedback. Int. J. Robust Nonlinear Control 30(13), 5134–5156 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  26. Z. Ding, Consensus control of a class of Lipchitz nonlinear systems. Int. J. Control 87(11), 2372–2382 (2014)

    MATH  Google Scholar 

  27. B. Zhou, G. Duan, Z. Lin, A parametric Lyapunov equation approach to the design of low gain feedback. IEEE Trans. Autom. Control 53(6), 1548–1554 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  28. B. Zhou, Z. Lin, G.R. Duan, Properties of the parametric Lyapunov equation-based low-gain design with applications in stabilization of time-delay systems. IEEE Trans. Autom. Control 54(7), 1698–1704 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  29. M.S. Sarafraz, M.S. Tavazoei, A unified optimization-based framework to adjust consensus convergence rate and optimize the network topology in uncertain multi-agent systems. IEEE/CAA J. Autom. Sin. 8(9), 1539–1548 (2021)

    Article  MathSciNet  Google Scholar 

  30. F. Golestani, M.S. Tavazoei, Delay-independent regulation of blood glucose for type-1 diabetes mellitus patients via an observer-based predictor feedback approach by considering quantization constraints. Eur. J. Control. 63, 240–252 (2022)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Electrical Engineering Department, Sharif University of Technology, Tehran, Iran

    Farzaneh Golestani & Mohammad Saleh Tavazoei

Authors
  1. Farzaneh Golestani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammad Saleh Tavazoei
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

FG methodology, software, draft manuscript preparation. MST conceptualization, draft manuscript preparation, supervision.

Corresponding author

Correspondence to Mohammad Saleh Tavazoei.

Ethics declarations

Conflict of interest

No conflict of interest exists regarding the publication of this work.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Golestani, F., Tavazoei, M.S. Event-based consensus control of Lipschitz nonlinear multi-agent systems with unknown input delay and quantization constraints. Eur. Phys. J. Spec. Top. 231, 3977–3985 (2022). https://doi.org/10.1140/epjs/s11734-022-00634-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-022-00634-2

Search

Navigation