SpringerLink
Log in

Event-triggered Consensus for Second-order Multi-agent Systems via Asynchronous Periodic Sampling Control Approach

  • Regular Papers
  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper focuses on asynchronous periodic sampling consensus for leader-following second-order multi-agent systems with event-triggered mechanism for the first time. A distributed control protocol is proposed to improve consistency and to reduce data transmission. We prove that the proposed algorithm is exponentially convergent if the topology contains a directed spanning tree. We acquire the consensus in two situations with the proposed controllers. (i) In the first situation, the positions converge to a nonzero constant and the velocities converge to zero when the velocity of the leader is zero; (ii) In the second situation, the errors of the positions and velocities between the followers and the virtual leader converge to a small region containing 0 when the velocity of the leader is a nonzero constant or time-varying. Finally, a numerical example with three cases is given to illustrate the effectiveness of the proposed asynchronous periodic sampling control method

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. W. W. Yu, G. R. Chen, Z. D. Wang, and W. Yang, “Distributed consensus filtering in sensor networks,” IEEE Transactions on Systems, vol. 39, no. 6. pp. 1568–1577, December 2009.

    Google Scholar 

  2. K. S. Hong and C. S. Kim, “Linear stable systems,” IEEE Transactions on Automatic Control, vol. 33, no. 3, pp. 1234–1245, December 1993.

    Google Scholar 

  3. W. Ren, “Multi-vehicle consensus with a time-varying reference state,” Systems and Control Letters, vol. 56, pp. 474–483, January 2007.

    MathSciNet  MATH  Google Scholar 

  4. Y. C. Cao, W. W. Yu, W. Ren, and G. R. Chen, “An overview of recent progress in the study of distributed multi-agent coordination,” IEEE Transactions on Industrial Informatics, vol. 9, no. 1, pp. 427–438, February 2013.

    Google Scholar 

  5. Y. Tang, X. **ng, H. R. Karimi, L. Kocarev and J. Kurths, “Trcaking control of networked multi-agent systems under new characterizations of impulses and its applications in robotic systems,” IEEE Transactions on Industrial Electronics, vol. 63, no. 2, pp. 1299–1307, February 2016.

    Google Scholar 

  6. S. Cheng, L. Yu, D. M. Zhang, and L. J. Huo, “Consensus of second-order multi-agent systems using partial agents’ velocity measurements,” Nonlinear Dynamics, vol. 86, no. 3, pp. 1927–1935, November 2016.

    MATH  Google Scholar 

  7. S. Cheng, L. Yu, D. M. Zhang, and J. C. Ji, “Consensus of multiple Euler-Lagrange systems using one Euler-Lagrange System’s velocity measurements,” International Journal of Control, Automation, and Systems, vol. 15, no. 1, pp. 450–456, February 2017.

    Google Scholar 

  8. S. Monaco and L. R. Celsi, “On multi-consensus and almost equitable graph partitions,” Automatica, vol. 103, pp. 53–61, May 2019.

    MathSciNet  MATH  Google Scholar 

  9. A. Pietrabissa and L. R. Celsi, “Discrete-time selfish routing converging to the wardrop equilibrium,” IEEE Transactions on Automatic Control, vol. 64, pp. 1288–1294, March 2019.

    MathSciNet  MATH  Google Scholar 

  10. G. S. Seyboth, D. V. Dimarogonas, and K. H. Johansson, “Event-based broadcasting for multi-agent average consensus,” Automatica, vol. 49, no. 1, pp. 245–252, January 2013.

    MathSciNet  MATH  Google Scholar 

  11. H. Ch. Yan, Y. Ch. Shen, H. Zhang, and H. B. Shi, “Decentralized event-triggered consensus control for second-order multi-agent systems,” Neurocomputing, vol. 133, pp. 18–24, June 2014.

    Google Scholar 

  12. D. S. **e, D. M. Yuan, J. W. Lu, and Y. J. Zhang, “Consensus control of second-order leader-follower multi-agent systems with event-triggered strategy,” Transactions of the Institute of Measurement and Control, vol. 35, no. 4, pp. 426–436, June 2013.

    Google Scholar 

  13. J. P. Hu, G. R. Chen, and H. X. Li, “Distributed eventtriggered tracking control of second-order leader-follower multi-agent systems,” Proceedings of the 30th Chinese Control Conference, pp. 4819–4824, July 2011.

    Google Scholar 

  14. Y. C. Cao and W. Ren, “Multi-vehicle coordination for double-integrator dynamics under fixed undirected/directed interaction in a sampled-data setting,” International Journal of Robust and Nonlinear Control, vol. 20, no. 9, pp. 987–1000, Janary 2009.

    MathSciNet  MATH  Google Scholar 

  15. Y. Q. Zhou, D. W. Li, Y. G. **, and Z. X. Gan, “Periodic event-triggered control for distributed networked multiagents with asynchronous communication: a predictive control approach,” International Journal of Robust and Nonlinear Control, vol. 29, no. 1, pp. 43–66, January 2019.

    MathSciNet  MATH  Google Scholar 

  16. L. Sh. Hu, T. Bai, P. Shi, and Z. M. Wu, “Sampled-data control of networked linear control systems,” Automatica, vol. 43, no. 5, pp. 903–911, may 2007.

    MathSciNet  MATH  Google Scholar 

  17. Y. Q. Wu, H. Y. Su, Peng Shi, Zh. Shu, and Zh. G. Wu, “Consensus of multi-agent mystems using aperiodic sampled-data control,” IEEE Transactions on Cybernetics, vol. 46, no. 9, pp. 2132–2143, September 2016.

    Google Scholar 

  18. W. Yu, L. Zhou, X. H. Yu, J. H. Lv, and R. Q. Lu, “Consensus in multi-agent systems with second-order dynamics and sampled data,” IEEE Transactions on Industrial Informatics, vol. 9, no. 4, pp. 2137–2146, November 2013.

    Google Scholar 

  19. H. Y. Liu and G. M. **e, “Sampled-data based containment control of continuous-time multi-agent systems with swithching topology and time-delays,” Neurocomputing, vol. 286, pp. 19–30, April 2018.

    Google Scholar 

  20. Y. T. Wang and Q. Sun, “Sampled-data collective rotating consensus for second-order networks under directed interaction,” International Journal of Control, Automation, and Systems, vol. 13, no. 5, pp. 1057–1066, July 2015.

    Google Scholar 

  21. B. Zhou and X. F. Liao, “Leader-following second-order consensus in multi-agent systems with sampled data via pinning control,” Nonlinear Dynamics, vol. 78, no. 1 pp. 555–569, June 2014.

    MathSciNet  MATH  Google Scholar 

  22. G. M. **e, H. Y. Liu, L. Wang, and Y. M. Jia, “Consensus in networked multi-agent systems via sampled control: fixed topology case,” American Control Conference, July 2009.

    Google Scholar 

  23. F. **ao and T. W. Chen, “Sampled-data consensus for multiple double integrators with arbitrary sampling,” IEEE Transactions on Automatic Control, vol. 57, no. 12, pp. 3230–3235, December 2012.

    MathSciNet  MATH  Google Scholar 

  24. G. Guo, L. Ding, and Q. L. Han, “A distributed eventtriggered transmission strategy for sampled-data consensus of multi-agent systems,” Automatica, vol. 50, no. 5, pp. 1489–1496, May 2014.

    MathSciNet  MATH  Google Scholar 

  25. H. Q. Li, X. F. Liao, T. W. Huang, and W. Zhu, “Eventtriggering sampling based leader-following consensus in second-order multi-agent systems,” IEEE Trancations on automatic control, vol. 60, no. 7, pp. 1998–2003, July 2015.

    MATH  Google Scholar 

  26. L. Y. Zhang, M. Chen, H. S. Su, and G. R. Chen, “Eventbased asynchronous communication and sampled control for synchronization of multiagent networks with input saturation,” International Journal of Robust and Nonlinear Control, vol. 28, no. 5, pp. 1871–1885, March 2018.

    MathSciNet  MATH  Google Scholar 

  27. B. X. Mu, K. W. Zhang, F. **ao and Y. Shi, “Eventbased rendezvous control for a group of robots with asynchronous periodic detection and communication time delays,” IEEE Transactions on Cybernetics, pp. 1–10, July 2018.

    Google Scholar 

  28. E. Aranda-Escolástico, C. Rodríguez, M. Guinaldo, J. L. Guzmánc, and D. Dormido, “Asynchronous periodic eventtriggered control with dynamical controllers,” Journal of the Franklin Institute, vol. 355, no. 8, pp. 3455–3469, May 2018.

    MathSciNet  MATH  Google Scholar 

  29. B. Zhou and X. Liao, “Leader-following second-order consensus in multi-agent systems with sampled data via pinning control,” Nonlinear Dynamics, vol. 78, pp. 555–569, 2014.

    MathSciNet  MATH  Google Scholar 

  30. H. Liu, L. Cheng, M. Tan, and Z. Hou, “Containment control of continuous-time linear multi-agent systems with aperiodic sampling,” Automatica, vol. 57, pp. 78–84, 2015.

    MathSciNet  MATH  Google Scholar 

  31. M. Cao, F. **ao, and L. Wang, “Second-order consensus in time-delayed networks based on periodic edge-event driven control,” Systems and Control Letters, vol. 96, pp. 37–44, 2016.

    MathSciNet  MATH  Google Scholar 

  32. J. Y. Zhan and X. Li, “Asynchronous consensus of multiple double-integrator agents with arbitrary sampling intervals and communication delays,” IEEE Transations on Circuits Systems-I: Regular Paper, vol. 62, no. 9, pp. 2301–2311, September 2015.

    MathSciNet  Google Scholar 

  33. X. Y. Meng, L. H. **e, and Y. C. Soh, “Asynchronous Periodic Event-triggered Consensus for Multi-agent Systems,” Automatica, vol. 84, pp. 214–220, August 2017.

    MathSciNet  MATH  Google Scholar 

  34. Y. P. Guan, Q. L. Han, and X. H. Ge, “On asynchronous event-triggered control of decentralized networked systems,” Information Sciences, vol. 425, pp. 127–139, January 2018.

    MathSciNet  Google Scholar 

  35. E. Aranda-Escolástico, C. Rodríguez, M. Guinaldo, J. L. Guzmán and S. Dormido, “Asynchronous periodic eventtriggered control with dynamical controllers,” Journal of the Franklin Institute, vol. 355, pp. 3455–3469, March 2018.

    MathSciNet  MATH  Google Scholar 

  36. Z. Y. Meng, W. Ren, Y. C. Cao, and Z. You, “Leaderless and leader-following consensus with communication and input delays under a directed network topology,” IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics, vol. 41, no. 1, pp. 75–88, February 2011.

    Google Scholar 

  37. Y. Cao, W. Ren, and Y. Li, “Distributed discrete-time coordinated tracking with a time-varying reference state and limited communication,” Automatca, vol. 45, pp. 1299–1305, 2009.

    MathSciNet  MATH  Google Scholar 

  38. W. W. Yu, G. R. Chen, and M. Cao, “Some necessary and sufficient conditions for second-order consensus in multiagent dynamical systems,” Automatica, vol. 46, no. 6, pp. 1089–1095, June 2010.

    MathSciNet  MATH  Google Scholar 

  39. D. Zheng, Linear System Theory, Tsinghua University Press, Bei**g, China, 2002.

    Google Scholar 

  40. W. W. Yu, “A LMI-based approach to global asymptotic stability of neural networks with time varing delays,” Nonlinear Dynamics, vol. 48, no. 1, pp. 165–174, April 2007.

    MathSciNet  MATH  Google Scholar 

  41. Y. G. Sun, L. Wang, and G. M. **e, “Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays,” Systems and Control Letters, vol. 57, pp. 175–183, 2008.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, **dian University, **’an, 710071, China

    Qing-Quan Yang, **g Li & **angchu Feng

  2. College of Mathematics and Information Science, **anyang Normal University, Shaanxi, China

    Shuiyan Wu

  3. College of Electronic Information Engineering, Inner Mongolia University, Hohhot, China

    Fei Gao

Authors
  1. Qing-Quan Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. **g Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. **angchu Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shuiyan Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Fei Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to **g Li.

Additional information

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

Recommended by Associate Editor Augie Widyotriatmo under the direction of Editor Myo Taeg Lim.

Qing-Quan Yang received her B.Sc. degree from the Department of Mathematics, Henan Institute of Engineering, Zhengzhou, China, in 2012, her M.Sc. degree in the School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China, in 2015. She is currently a Ph. D. Candidate with the School of Mathematics and Statistics, **dian University, **’an, China. Her current research interests include multi-agent systems, nonlinear systems, distributed strategy, and switching control.

**g Li received her B.S. degree in Mathematics in 2001 from Henan University, Kaifeng, China, and received her M.Sc. segree in Operational Research and Cybernetics in 2004 and the Ph.D. degree in applied mathematics in 2010 from **dian University, **’an, China, respectively. From Sep. 2009 to Jul. 2010, she was a Visiting Scholar at the School of Control Science and Engineering, Shandong University, **an, China. From Oct. 2011 to Oct. 2012, she was an Academic Visitor in Robotics at Plymouth University, Plymouth, UK and in human robot interaction at Imperial College London, London, UK, simultaneously. She is currently a Professor at the School of Mathematics and Statistics, **dian University, **’an, China. Her current research interests include adaptive control, neural network control, multi-agent systems, switching control, and humanrobot interaction.

**angchu Feng received his B.S. degree in Computational Mathematics from the **’an JiaoTong University, **’an, China, in 1984, and his M.S. and Ph.D. degrees in Applied Mathematics from **dian University, **’an, in 1989 and 1999, respectively. He is currently a Professor with the School of Mathematics and Statistics, **dian University. His research interests include numerical analysis, wavelets, and partial differential equations for image processing.

Shuiyan Wu received her B.S. degree in mathematics from Henan University, Kaifeng, China, in 2001, and her M.Sc. degree in Applied Mathematics from **dian University, **’an, China, in 2010. Now she is a lecturer with the College of Mathematics and Information Science, **anyang Normal University, Shaanxi, China. Her current research interest focuses on optimization theory.

Fei Gao received his B.Sc. degree in measurement and control technology and instrumentation, his M.Sc. degree in instrumentation engineering and a Ph.D. degree in control theory and control engineering from **dian University, **’an, China, in 2012, 2016, and 2019, respectively. He is currently with the college of electronic information engineering, Inner Mongolia University, Hohhot, China. His current research interests include multi-agent systems, adaptive neural control and nonlinear systems.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, QQ., Li, J., Feng, X. et al. Event-triggered Consensus for Second-order Multi-agent Systems via Asynchronous Periodic Sampling Control Approach. Int. J. Control Autom. Syst. 18, 1399–1411 (2020). https://doi.org/10.1007/s12555-019-0137-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-019-0137-y

Keywords

Search

Navigation