Skip to main content
SpringerLink
Log in

Event-triggered average-consensus of multi-agent systems with weighted and direct topology

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

This paper investigates the average-consensus problem of multi-agent systems with direct and weighted topologies. Event-triggered control laws are adopted so as to reduce the frequency of individual control updating since the agents may be resource-limited in many real systems. The discrete time instants where the events are triggered are determined by a trigger function with respect to a certain measurement error. A centralized average-consensus protocol is proposed first for networks with fixed interaction topology, the stability and influencing factors of which are also analyzed. The design of trigger functions for networks with variable topology is also discussed. Then the results are extended to the decentralized counterpart, in which agents require only the information of their neighbors. Numerical examples are also provided that demonstrate the effectiveness of the theoretical 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

Similar content being viewed by others

References

  1. A. Jadbabie, J. Lin, and A. S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transactions on Automatic Control, 2003, 48(6): 988–1001.

    Article  Google Scholar 

  2. R. Olfati-Saber and R. M. Murray, Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control, 2004, 49(9): 1520–1533.

    Article  MathSciNet  Google Scholar 

  3. L. Moreau, Stability of multiagent systems with time-dependent communication links, IEEE Transactions on Automatic Control, 2005, 50(2): 169–182.

    Article  MathSciNet  Google Scholar 

  4. Y. Hong, J. Hu, and L. Gao, Tracking control for multi-agent consensus with an active leader and variable topology, Automatica, 2006, 42(7): 1177–1182.

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Porfiria, D. G. Robersonb, and D. J. Stilwell, Tracking and formation control of multiple autonomous agents: A two-level consensus approach, Automatica, 2007, 43(8): 1318–1328.

    Article  MathSciNet  Google Scholar 

  6. R. Olfati-Saber, J. A. Fax, and R. M. Murray, Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 2007, 95(1): 215–233.

    Article  Google Scholar 

  7. F. Xiao and L. Wang, Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays, IEEE Transactions on Automatic Control, 2008, 53(8): 1804–1816.

    Article  MathSciNet  Google Scholar 

  8. A. Olshevsky and J. N. Tsitsiklis, On the nonexistence of quadratic lyapunov function for consensus algorithms, IEEE Transactions on Automatic Control, 2008, 53(11): 2642–2645.

    Article  MathSciNet  Google Scholar 

  9. L. Wang, Z. Chen, Z. Liu, and Z. Yuan, Finite time agreement protocol design on multi-agent system with communication delays, Asian Journal of Control, 2009, 11(3): 281–286.

    Article  MathSciNet  Google Scholar 

  10. F. Chen, Z. Chen, L. Xiang, Z. Liu, and Z. Yuan, Reaching a consensus via pinning control, Automatica, 2009, 45(5): 1215–1220.

    Article  MathSciNet  MATH  Google Scholar 

  11. W. Guo, S. Chen, J. Lü, and X. Yu,: Consensus of multi-agent systems with an active leader and asymmetric adjacency matrix, the 48th IEEE Conference on Decision and Control and the 28th Chinese Control Conference, Shanghai, P. R. China, December, 2009.

  12. Y. Chen, J. Lü, and Z. Lin, Consensus of discrete-time multi-agent systems with nonlinear local rules and time-varying delays, in Joint the 48th IEEE Conference on Decision and Control and the 28th Chinese Control Conference, Shanghai, P. R. China, December, 2009.

  13. W. Ren, Consensus tracking under directed interaction topologies: Algorithms and experiments, IEEE Transactions on Control Systems Technology, 2010, 18(1): 230–237.

    Article  Google Scholar 

  14. C. Ma, T. Li, and J. Zhang, Consensus control for leader-following multi-agent systems with measurement noises, Journal of Systems Science & Complexity, 2010, 23(1): 35–49.

    Article  MathSciNet  Google Scholar 

  15. X. Wang and Y. Hong, Distributed finite-time χ-consensus algorithms for multi-agent systems with variable coupling topology, Journal of Systems Science & Complexity, 2010, 23(2): 209–218.

    Article  MathSciNet  Google Scholar 

  16. P. Tabuada, Event-triggered real-time scheduling of stabilizing control tasks, IEEE Transactions on Automatic Control, 2007, 52(9): 1680–1685.

    Article  MathSciNet  Google Scholar 

  17. W. P. M. H. Heemels, J. H. Sandee, and P. P. J. Van Den Bosch, Analysis of event-driven controllers for linear systems, International Journal of Control, 2008, 81(4): 571–590.

    Article  MathSciNet  MATH  Google Scholar 

  18. X. Wang and M. D. Lemmon, Event-triggered broadcasting across distributed networked control systems, in the 2008 American Control Conference, Washington, USA, June, 2008.

  19. M. M. Jr. and P. Tabuada, On event-triggered and self-triggered control over sensor/actuator networks, in the 47th IEEE Conference on Decision and Control, Cancun, Mexico, December, 2008.

  20. D. V. Dimarogonas and K. H. Johansson, Event-triggered control for multi-agent systems, in Joint the 48th IEEE Conference on Decision and Control and the 28th Chinese Control Conference, Shanghai, P.R. China, December, 2009.

  21. D. V. Dimarogonas and K. H. Johansson, Event-triggered cooperative control, in the 2009 European Control Conference, Budapest, Hungary, August, 2009.

  22. X. Wang and M. D. Lemmon, Self-triggered feedback control systems with finite-gain l2 stability, IEEE Transactions on Automatic Control, 2009, 54(3): 452–467.

    Article  MathSciNet  Google Scholar 

  23. J. Lunze and D. Lehmann, A state-feedback approach to event-based control, Automatica, January 2010, 46(1): 211–215.

    Google Scholar 

  24. E. D. Sontag and Y. Wang, On characteizations of the input-to-state stability property, Systems and Control Letters, 1995, 24: 351–359.

    Article  MathSciNet  MATH  Google Scholar 

  25. E. Sontag, On the input-to-state stability property, European Journal of Control, 1995, 1: 24–36.

    MATH  Google Scholar 

  26. K. H. Johansson, M. Egerstedt, J. Lygeros, and S. S. Sastry, On the regularization of zeno hybrid automata, Systems and Control Letters, 1999, 38: 141–150.

    Article  MathSciNet  MATH  Google Scholar 

  27. C. Godsil and G. Royle, Algebraic Graph Theory, volume 207 of Graduate Texts in Mathematics, Berlin, Germany: Springer-Verlag, 2001.

    Google Scholar 

  28. J. Lygeros, K. H. Johansson, S. Simic, J. Zhang, and S. Sastry, Dynamical properties of hybrid automata, IEEE Transactions on Automatic Control, 2003, 48(1): 2–17.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Automation, Nankai University, Tianjin, 300071, China

    Zhongxin Liu, Zengqiang Chen & Zhuzhi Yuan

Authors
  1. Zhongxin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zengqiang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhuzhi Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhongxin Liu.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant No. 60904064, 61174094, the Program for New Century Excellent Talents in University of China (NCET-10-0506), and the Tianjin Natural Science Foundation of China under Grant No. 09JCYBJC01700.

This paper was recommended for publication by Editor Jinhu LÜ.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, Z., Chen, Z. & Yuan, Z. Event-triggered average-consensus of multi-agent systems with weighted and direct topology. J Syst Sci Complex 25, 845–855 (2012). https://doi.org/10.1007/s11424-012-0116-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-012-0116-3

Key words

Search

Navigation