New Event-based Control for Sampled-data Consensus of Multi-agent Systems

  • Long Jian
  • Jiangping Hu
  • Jun Wang
  • Kaibo ShiEmail author


This paper investigates the sampled-data consensus problem of general linear multi-agent systems via new event-based control. Both the leaderless and leader-following consensus problems are considered. Different from the existing results, the state information is assumed to be unknown for each following agent and only the relative output information between neighbouring agents can be measured. A new Kx-functional observer-based output feedback event-based protocol is designed, which may have lower dimension than the full-order and reducedorder observer. The improved event-based condition bounds each agent’s measurement error by a time-dependent threshold. Furthermore, the Zeno behavior is excluded by showing that the inter-event time between any two triggering events is lower bounded by a strictly positive value. Finally, a numerical simulation example is presented to demonstrate the effectiveness of the proposed control protocols.


Event-based control Kx-functional observer multi-agent systems sampled-data consensus 


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  1. [1]
    K. Shi, Y. Y. Tang, X. Liu, and S. Zhong, “Non-fragile sampled-data robust synchronization of uncertain delayed chaotic lurie systems with randomly occurring controller gain fluctuation,” ISA Transactions, vol. 66, no. 66, pp. 185–199, 2017.CrossRefGoogle Scholar
  2. [2]
    K. Shi, Y. Tang, S. Zhong, C. Yin, X. Huang, and W. Wang, “Nonfragile asynchronous control for uncertain chaotic lurie network systems with bernoulli stochastic process,” International Journal of Robust & Nonlinear Control, vol. 28, no. 5, pp. 1693–1714, 2018.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    J. Wang, K. Shi, Q. Huang, S. Zhong, and D. Zhang, “Stochastic switched sampled-data control for synchronization of delayed chaotic neural networks with packet dropout,” Applied Mathematics and Computation, vol. 335, pp. 211–230, 2018.MathSciNetCrossRefGoogle Scholar
  4. [4]
    T. H. Lee and H. P. Ju, “Improved criteria for sampled-data synchronization of chaotic lur’e systems using two new approaches,” Nonlinear Analysis Hybrid Systems, vol. 24, pp. 132–145, 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    T. H. Lee, Z. G. Wu, and H. P. Ju, “Synchronization of a complex dynamical network with coupling time-varying delays via sampled-data control,” Applied Mathematics & Computation, vol. 219, no. 3, pp. 1354–1366, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    H. Shen, F. Li, S. Xu, and V. Sreeram, “Slow state variables feedback stabilization for semi-markov jump systems with singular perturbations,” IEEE Trans. on Automatic Control, vol. 63, no. 8, pp. 2709–2714, 2018.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    H. Shen, Y. Zhu, L. Zhang, and J. H. Park, “Extended dis-sipative state estimation for Markov jump neural networks with unreliable links,” IEEE Trans. on Neural Networks, vol. 28, no. 2, pp. 346–358, 2017.MathSciNetCrossRefGoogle Scholar
  8. [8]
    H. Shen, S. Huo, J. Cao, and T. Huang, “Generalized state estimation for markovian coupled networks under round-robin protocol and redundant channels,” IEEE Trans. on Systems, Man, and Cybernetics, vol. 49, no. 4, pp. 1292–1301, 2018.Google Scholar
  9. [9]
    R. OlfatiSaber and R. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Trans. on Automatic Control, vol. 49, no. 9, pp. 1520–1533, 2004.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Y. Hong, J. Hu, and L. Gao, “Tracking control for multi-agent consensus with an active leader and variable topology,” Automatica, vol. 42, no. 7, pp. 1177–1182, 2006.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    W. Ni and D. Cheng, “Leader-following consensus of multi-agent systems under fixed and switching topologies,” Systems & Control Letters, vol. 59, no. 3–4, pp. 209–217, 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    D. V. Dimarogonas, E. Frazzoli, and K. H. Johansson, “Distributed event-triggered control for multi-agent systems,” IEEE Trans. on Automatic Control, vol. 57, no. 5, pp. 1291–1297, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    W. Hu, L. Liu, and G. Feng, “Consensus of linear multi-agent systems by distributed event-triggered strategy,” IEEE Trans. on Cybernetics, vol. 46, no. 1, pp. 148–157, 2016.CrossRefGoogle Scholar
  14. [14]
    T. H. Cheng, Z. Kan, J. R. Klotz, J. M. Shea, and W. E. Dixon, “Event-triggered control of multi-agent systems for fixed and time-varying network topologies,” IEEE Trans. on Automatic Control, vol. 62, no. 10, pp. 5365–5371, 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    J. Y. Liu, W. S. Chen, and H. Dai, “Sampled-data based distributed convex optimization with event-triggered communication,” International Journal of Control, Automation, and Systems, vol. 14, no. 6, pp. 1–9, 2016.CrossRefGoogle Scholar
  16. [16]
    G. Guo, L. Ding, and Q. L. Han, “A distributed event-triggered transmission strategy for sampled-data consensus of multi-agent systems,” Automatica, vol. 50, no. 5, pp. 1489–1496, 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    J. Hu, G. Chen, and H. X. Li, “Distributed event-triggered tracking control of leader-follower multi-agent systems with communication delays,” Kybernetika, vol. 4, no. 4, pp. 630–643, 2011.MathSciNetzbMATHGoogle Scholar
  18. [18]
    Y. Fan, L. Liu, G. Feng, and Y. Wang, “Self-triggered consensus for multi-agent systems with zeno-free triggers,” IEEE Trans. on Automatic Control, vol. 60, no. 10, pp. 2779–2784, 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    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, 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    W. Zhu, Z. P. Jiang, and G. Feng, “Event-based consensus of multi-agent systems with general linear models,” Auto-matica, vol. 50, no. 2, pp. 552–558, 2014.MathSciNetzbMATHGoogle Scholar
  21. [21]
    D. Yang, W. Ren, X. Liu, and W. Chen, “Decentralized event-triggered consensus for linear multi-agent systems under general directed graphs,” Automatica, vol. 69, no. 69, pp. 242–249, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    B. Cheng and Z. Li, “Fully distributed event-triggered protocols for linear multi-agent networks,” IEEE Trans. on Automatic Control, 2018. DOI: 10.1109/TAC.2018.2857723Google Scholar
  23. [23]
    X. Wang and M. D. Lemmon, “Event-triggering in distributed networked control systems,” IEEE Trans. on Automatic Control, vol. 56, no. 3, pp. 586–601, 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    C. Nowzari and J. Cortés, “Distributed event-triggered coordination for average consensus on weight-balanced digraphs,” Automatica, vol. 68, no. 68, pp. 237–244, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    E. Garcia, Y. Cao, and D. W. Casbeer, “Decentralized event-triggered consensus with general linear dynamics,” Automatica, vol. 50, no. 10, pp. 2633–2640, 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    Z. Tang, “Event-triggered consensus of linear discrete-time multi-agent systems with time-varying topology,” International Journal of Control, Automation, and Systems, vol. 16, no. 3, pp. 1179–1185, 2018.CrossRefGoogle Scholar
  27. [27]
    Z. Tang and C. Li, “Distributed event-triggered containment control for discrete-time multi-agent systems,” International Journal of Control, Automation, and Systems, vol. 16, no. 6, pp. 2727–2732, 2018.CrossRefGoogle Scholar
  28. [28]
    J. Hu and W. X. Zheng, “Adaptive tracking control of leader-follower systems with unknown dynamics and partial measurements,” Automatica, vol. 50, no. 5, pp. 1416–1423, 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    Z. Li, Z. Duan, G. Chen, and L. Huang, “Consensus of mul-tiagent systems and synchronization of complex networks: a unified viewpoint,” IEEE Trans. on Circuits & Systems I Regular Papers, vol. 57, no. 1, pp. 213–224, 2010.MathSciNetCrossRefGoogle Scholar
  30. [30]
    X. Xu, S. Chen, and L. Gao, “Observer-based consensus tracking for second-order leader-following nonlinear multi-agent systems with adaptive coupling parameter design,” Neurocomputing, vol. 156, pp. 297–305, 2015.CrossRefGoogle Scholar
  31. [31]
    Y. Wu and J. Hu, “Observer-based output regulation of cooperative-competitive high-order multi-agent systems,” Journal of The Franklin Institute, vol. 355, no. 10, pp. 4111–4130, 2018.MathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    Y. Wu, J. Hu, Y. Zhang, and Y. Zeng, “Interventional consensus for high-order multi-agent systems with unknown disturbances on coopetition networks,” Neurocomputing, vol. 194, no. 194, pp. 126–134, 2016.CrossRefGoogle Scholar
  33. [33]
    J. Hu, Y. Wu, T. Li and B. K. Ghosh, “Consensus control of general linear multi-agent systems with antagonistic interactions and communication noises,” IEEE Trans. on Automatic Control, 2018. DOI: 10.1109/TAC.2018.2872197Google Scholar
  34. [34]
    Z. Li, X. Liu, P. Lin, and W. Ren, “Consensus of linear multi-agent systems with reduced-order observer-based protocols,” Systems & Control Letters, vol. 60, no. 7, pp. 510–516, 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    B. Zhou, C. Xu, and G. Duan, “Distributed and truncated reduced-order observer based output feedback consensus of multi-agent systems,” IEEE Trans. on Automatic Control, vol. 59, no. 8, pp. 2264–2270, 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    Y. Hu, J. Lam, and J. Liang, “Consensus of multi-agent systems with luenberger observers,” Journal of the Franklin Institute, vol. 350, no. 9, pp. 2769–2790, 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    J. Zhang and G. Feng, “Event-driven observer-based output feedback control for linear systems,” Automatica, vol. 50, no. 7, pp. 1852–1859, 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  38. [38]
    D. Ding, Z. Wang, D. W. Ho, and G. Wei, “Observer-based event-triggering consensus control for multiagent systems with lossy sensors and cyber-attacks,” IEEE Trans. on Cybernetics, vol. 47, no. 8, pp. 1936–1947, 2017.CrossRefGoogle Scholar
  39. [39]
    J. Wang, P. Zhang, and W. Ni, “Observer-based event-triggered control for consensus of general linear mass,” IET Control Theory & Applications, vol. 11, no. 18, pp. 3305–3312, 2018.MathSciNetCrossRefGoogle Scholar
  40. [40]
    J. Hu, J. Geng, and H. Zhu, “An observer-based consensus tracking control and application to event-triggered tracking,” Communications in Nonlinear Science & Numerical Simulation, vol. 20, no. 2, pp. 559–570, 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    H. Zhang, G. Feng, H. Yan, and Q. Chen, “Observer-based output feedback event-triggered control for consensus of multi-agent systems,” IEEE Trans. on Industrial Electronics, vol. 61, no. 9, pp. 4885–4894, 2014.CrossRefGoogle Scholar
  42. [42]
    L. Gao, Y. Cui, X. Xu, and Y. Zhao, “Distributed consensus protocol for leader-following multi-agent systems with functional observers,” Journal of the Franklin Institute, vol. 352, no. 11, pp. 5173–5190, 2015.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.School of Automation EngineeringUniversity of Electronic Science and Technology of ChinaChengduP. R. China
  2. 2.College of Electrical and Information EngineeringSouthwest Minzu UniversityChengduP. R. China
  3. 3.School of Information Science and EngineeringChengdu UniversityChengduP. R. China

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