Journal of Systems Science and Complexity

, Volume 25, Issue 5, pp 845–855 | Cite as

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

Article

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.

Key words

Average-consensus consensus digraph event-triggered control multi-agent system 

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References

  1. [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.CrossRefGoogle Scholar
  2. [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.MathSciNetCrossRefGoogle Scholar
  3. [3]
    L. Moreau, Stability of multiagent systems with time-dependent communication links, IEEE Transactions on Automatic Control, 2005, 50(2): 169–182.MathSciNetCrossRefGoogle Scholar
  4. [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.MathSciNetMATHCrossRefGoogle Scholar
  5. [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.MathSciNetCrossRefGoogle Scholar
  6. [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.CrossRefGoogle Scholar
  7. [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.MathSciNetCrossRefGoogle Scholar
  8. [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.MathSciNetCrossRefGoogle Scholar
  9. [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.MathSciNetCrossRefGoogle Scholar
  10. [10]
    F. Chen, Z. Chen, L. Xiang, Z. Liu, and Z. Yuan, Reaching a consensus via pinning control, Automatica, 2009, 45(5): 1215–1220.MathSciNetMATHCrossRefGoogle Scholar
  11. [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.Google Scholar
  12. [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.Google Scholar
  13. [13]
    W. Ren, Consensus tracking under directed interaction topologies: Algorithms and experiments, IEEE Transactions on Control Systems Technology, 2010, 18(1): 230–237.CrossRefGoogle Scholar
  14. [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.MathSciNetCrossRefGoogle Scholar
  15. [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.MathSciNetCrossRefGoogle Scholar
  16. [16]
    P. Tabuada, Event-triggered real-time scheduling of stabilizing control tasks, IEEE Transactions on Automatic Control, 2007, 52(9): 1680–1685.MathSciNetCrossRefGoogle Scholar
  17. [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.MathSciNetMATHCrossRefGoogle Scholar
  18. [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.Google Scholar
  19. [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.Google Scholar
  20. [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.Google Scholar
  21. [21]
    D. V. Dimarogonas and K. H. Johansson, Event-triggered cooperative control, in the 2009 European Control Conference, Budapest, Hungary, August, 2009.Google Scholar
  22. [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.MathSciNetCrossRefGoogle Scholar
  23. [23]
    J. Lunze and D. Lehmann, A state-feedback approach to event-based control, Automatica, January 2010, 46(1): 211–215.Google Scholar
  24. [24]
    E. D. Sontag and Y. Wang, On characteizations of the input-to-state stability property, Systems and Control Letters, 1995, 24: 351–359.MathSciNetMATHCrossRefGoogle Scholar
  25. [25]
    E. Sontag, On the input-to-state stability property, European Journal of Control, 1995, 1: 24–36.MATHGoogle Scholar
  26. [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.MathSciNetMATHCrossRefGoogle Scholar
  27. [27]
    C. Godsil and G. Royle, Algebraic Graph Theory, volume 207 of Graduate Texts in Mathematics, Berlin, Germany: Springer-Verlag, 2001.Google Scholar
  28. [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.MathSciNetCrossRefGoogle Scholar

Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of AutomationNankai UniversityTianjinChina

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