Skip to main content
SpringerLink
Log in

Finite-time average consensus of directed second-order multi-agent systems with Markovian switching topology and impulsive disturbance

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

This paper investigates finite-time mean square average consensus of second-order multi-agent systems, where connected typologies are directed and subject to Markovian switching, agents dynamics are nonlinear and interrupt by impulses. In order to eliminate the chattering phenomenon in finite-time control, we propose a protocol without sign function, that contains neighborhood and self state feedbacks. Also, by employing graph theory, some graph-related matrices are formed to analyze directed switching topologies. Then, expectations of multi-agent systems energy evolution are bounded in both continuous and discontinuous time by using stochastic and discontinuous stability theories. In this basis, sufficient finite-time mean square consensus criteria are established and their settling times are obtained. Simulation examples prove the theoretical results are correct and the finite-time protocol is valid.

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
Fig. 5

Similar content being viewed by others

Data availability

Data sharing is not applicable to this paper as no datasets were generated or analyzed during the current study.

References

  1. Olfati-Saber R, Fax J, Murray RM (2007) Consensus and cooperation in networked multi-agent systems. Proc IEEE 95(1):215–233

    Article  MATH  Google Scholar 

  2. Xiao F, Wang L (2007) Consensus problems for high-dimensional multi-agent systems. IET Control Theory Appl 1(3):830–837

    Article  Google Scholar 

  3. Li H, Liao X, Huang T, Zhu W (2015) Event-triggering sampling based leader-following consensus in second-order multi-agent systems. IEEE Trans Autom Control 60(7):1998–2003

    Article  MathSciNet  MATH  Google Scholar 

  4. Zhu Z, Guan Z, Hu B et al (2021) Semi-global bipartite consensus tracking of singular multi-agent systems with input saturation. Neurocomputing 432(7):183–193

    Article  Google Scholar 

  5. Zhao H, Peng L, Yu H (2021) Model-free adaptive consensus tracking control for unknown nonlinear multi-agent systems with sensor saturation. Int J Robust Nonlinear Control. https://doi.org/10.1002/rnc.5630

    Article  MathSciNet  Google Scholar 

  6. Li H, Chen G, Huang T, Dong Z (2017) High-performance consensus control in networked systems with limited bandwidth communication and time-varying directed topologies. IEEE Trans Neural Netw Learn Syst 28(5):1043–1054

    Article  Google Scholar 

  7. Zheng Y, Ma J, Wang L (2018) Consensus of hybrid multi-agent systems. IEEE Trans Neural Netw Learn Syst 29(4):1359–1365

    Article  Google Scholar 

  8. Gong P, Wang K, Lan W (2019) Fully distributed robust consensus control of multi-agent systems with heterogeneous unknown fractional-order dynamics. Int J Syst Sci 50(10):1902–1919

    Article  MathSciNet  MATH  Google Scholar 

  9. Ji L, Tong S, Li H (2021) Dynamic group consensus for delayed heterogeneous multi-agent systems in cooperative-competitive networks via pinning control[J]. Neurocomputing 443(5):1–11

    Google Scholar 

  10. Zhan J, Jiang Z, Wang Y, Li X (2019) Distributed model predictive consensus with self-triggered mechanism in general linear multiagent systems. IEEE Trans Ind Inf 15(7):3987–3997

    Article  Google Scholar 

  11. Yang X, Wu Z, Cao J (2013) Finite-time synchronization of complex networks with nonidentical discontinuous nodes. Nonlinear Dyn 73:2313–2327

    Article  MathSciNet  MATH  Google Scholar 

  12. Li Q, Wei J, Yuan J, Gou Q, Niu Z (2021) Distributed event-triggered adaptive finite-time consensus control for second-order multi-agent systems with connectivity preservation. J Franklin Inst 358(12):6013–6034

    Article  MathSciNet  MATH  Google Scholar 

  13. Cui Y, Liu X, Deng X, Wen G (2021) Command-filter-based adaptive finite-time consensus control for nonlinear strict-feedback multi-agent systems with dynamic leader. Inf Sci 565:17–31

    Article  MathSciNet  Google Scholar 

  14. Hu Z, Yang J (2018) Distributed finite-time optimization for second order continuous-time multiple agents systems with time-varying cost function. Neurocomputing 287:173–184

    Article  Google Scholar 

  15. Yao D, Dou C, Zhao N, Zhang T (2021) Finite-time consensus control for a class of multi-agent systems with dead-zone input. J Franklin Inst 358:3512–3529

    Article  MathSciNet  MATH  Google Scholar 

  16. Yang X, Lu J (2016) Finite-time synchronization of coupled networks with Markovian topology and impulsive effects. IEEE Trans Autom Control 61(8):2256–2261

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhang W, Li C, He X et al (2018) Finite-time synchronization of complex networks with non-identical nodes and impulsive disturbances. Mod Phys Lett B 32(1):1850002

    Article  MathSciNet  Google Scholar 

  18. Zhang W, Li C, Huang T et al (2018) Finite-time synchronization of neural networks with multiple proportional delays via non-chattering control. Int J Control Autom Syst 16:2473–2479

    Article  Google Scholar 

  19. Tian Y, Li C (2020) Finite-time consensus of second-order nonlinear multi-agent systems with impulsive effects. Mod Phys Lett B 34(35):2050406

    Article  MathSciNet  Google Scholar 

  20. Chen T, Peng S, Zhang Z (2021) Finite-time consensus of leader-following non-linear multi-agent systems via event-triggered impulsive control. IET Control Theory Appl 4(15):926–936

    Article  Google Scholar 

  21. Qin J, Yu C, Hirche S (2012) Stationary consensus of asynchronous discrete-time second-order multi-agent systems under switching topology. IEEE Trans Ind Inf 8(4):986–994

    Article  Google Scholar 

  22. Wu X, Tang Y, Cao J et al (2016) Distributed consensus of stochastic delayed multi-agent systems under asynchronous switching. IEEE Trans Cybern 46(8):1817–1827

    Article  Google Scholar 

  23. Franceschelli M, Giua A, Pisano A et al (2013) Finite-time consensus for switching network topologies with disturbances. Nonlinear Anal Hybrid Syst 10:83–93

    Article  MathSciNet  MATH  Google Scholar 

  24. Li W, Wu Z (2013) Output tracking of stochastic high-order nonlinear systems with Markovian switching. IEEE Trans Autom Control 58(6):1585–1590

    Article  MathSciNet  MATH  Google Scholar 

  25. Liu Q, Wang Z, He X et al (2019) Event-based distributed filtering over Markovian switching topologies. IEEE Trans Autom Control 64(4):1595–1602

    Article  MathSciNet  MATH  Google Scholar 

  26. Liang K, He W, Xu J, Qian F (2022) Impulsive effects on synchronization of singularly perturbed complex networks with semi-markov jump topologies. IEEE Trans Syst Man Cybern Syst 52(5):3163–3173

    Article  Google Scholar 

  27. He W, Qian F, Han Q et al (2020) Almost sure stability of nonlinear systems under random and impulsive sequential attacks. IEEE Trans Autom Control 65(9):3879–3886

    Article  MathSciNet  MATH  Google Scholar 

  28. Yu W, Chen G, Cao M, Kurths J (2010) Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics. IEEE Trans Syst Man Cybern Part B (Cybernetics) 40(3):881–891

    Article  Google Scholar 

  29. Yaz EE (1998) Linear matrix inequalities in system and control theory. Proc IEEE 86(12):2473–2474

    Article  Google Scholar 

  30. Mao X (2007) Stochastic differential equations and applications, 2nd edn. Woodhead Publishing, Cambridge

    MATH  Google Scholar 

  31. Zou W, Xiang Z, Ahn CK (2019) Mean square leader-following consensus of second-order nonlinear multiagent systems with noises and unmodeled dynamics. IEEE Trans Syst Man Cybern Syst 49(12):2478–2486

    Article  Google Scholar 

  32. Zhang J, Li T, Li T et al (2009) Mean square average-consensus under measurement noises and fixed topologies: necessary and sufficient conditions. Automatica 45(8):1929–1936

    Article  MathSciNet  MATH  Google Scholar 

  33. Yang T (2001) Impulsive control theory. Springer-Verlag, New York

    MATH  Google Scholar 

  34. Mariton M (1990) Jump linear systems in automatic control. Marcel Dekker, New York

    Google Scholar 

  35. Poss S (1996) Stochastic processes, 2nd edn. Wiley, New York

    Google Scholar 

  36. Chua LO, Pivka L, Wu C (1995) A universal circuit for studying chaotic phenomena. Philos Trans R Soc B Biol 353(1701):65–84

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grants No. 61173178, 61374078 and 61633011, the Science and Technology Research Program of Chongqing Municipal Education Commission in China Grant No.KJZD-K202100104 and Natural Science Foundation of Chongqing under Grant No.cstc2021jcyj-msxmX1212, China.

Author information

Authors and Affiliations

  1. College of Intelligent Technology and Engineering, Chongqing University of Science and Technology, Chongqing, 401331, People’s Republic of China

    Yuan Tian & Qi Han

  2. College of Electronic and Information Engineering, Southwest University, Chongqing, 400075, People’s Republic of China

    Huaqing Li

Authors
  1. Yuan Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huaqing Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qi Han
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuan Tian.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tian, Y., Li, H. & Han, Q. Finite-time average consensus of directed second-order multi-agent systems with Markovian switching topology and impulsive disturbance. Neural Comput & Applic 35, 8575–8588 (2023). https://doi.org/10.1007/s00521-022-08131-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-022-08131-2

Keywords

Search

Navigation