Kybernetika 56 no. 2, 217-238, 2020

Event-triggered output consensus for linear multi-agent systems via adaptive distributed observer

Limin Zhang, Jian Sun and Qingkai YangDOI: 10.14736/kyb-2020-2-0217


This paper investigates the distributed event-triggered cooperative output regulation problem for heterogeneous linear continuous-time multi-agent systems (MASs). To eliminate the requirement of continuous communication among interacting following agents, an event-triggered adaptive distributed observer is skillfully devised. Furthermore, a class of closed-loop estimators is constructed and implemented on each agent such that the triggering times on each agent can be significantly reduced while at the same time the desired control performance can be preserved. Compared with the existing open-loop estimators, the proposed estimators can provide more accurate state estimates during each triggering period. It is further shown that the concerned cooperative output regulation problem can be effectively resolved under the proposed control scheme and the undesirable Zeno behavior can be excluded. Finally, the effectiveness of the proposed results is verified by numerical simulations.


output regulation, event-triggered communication (ETC), cooperative control, multi-agent systems (MASs)




  1. W. Ren and N. Sorensen: Distributed coordination architecture for multi-robot formation control. Robotics Autonomous Systems 56 (2008), 324-333.   DOI:10.1016/j.robot.2007.08.005
  2. L. Vig and J.A. Adams: Multi-robot coalition formation. IEEE Trans. Robotics 22 (2006), 637-649.   DOI:10.1109/tro.2006.878948
  3. T. Arai, E. Pagello and L.E. Parker: Guest editorial Advances in multi-robot systems. IEEE Trans. Robotics Automat. 18 (2002), 655-661.   DOI:10.1109/tra.2002.806024
  4. X. Ge, Q.-L. Han and Z. Wang: A threshold-parameter-dependent approach to designing distributed event-triggered $H_\infty$ consensus filters over sensor networks. IEEE Trans. Cybernetics 49 (2019), 1148-1159.   DOI:10.1109/tcyb.2017.2789296
  5. Y. Guan and X. Ge: Distributed attack detection and secure estimation of networked cyber-physical systems against false data injection attacks and jamming attacks. IEEE Trans. Signal Inform. Process. Networks 4 (2018), 48-59.   DOI:10.1109/tcyb.2017.2789296
  6. X. Ge, Q.-L. Han, M. Zhong and X.-M. Zhang: Distributed Krein space-based attack detection over sensor networks under deception attacks. Automatica 109 (2019), 108557.   DOI:10.1016/j.automatica.2019.108557
  7. L. Ding, Q.-L. Han and X.-M. Zhang: Distributed secondary control for active power sharing and frequency regulation in islanded microgrids using an event-triggered communication mechanism. IEEE Trans. Industr. Inform. 15 (2019), 3910-3922.   DOI:10.1109/tii.2018.2884494
  8. D. Ding, Q.-L. Han, Z. Wang and X. Ge: A survey on model-based distributed control and filtering for industrial cyber-physical systems. IEEE Trans. Industr. Informatics 15 (2019), 2483-2499.   DOI:10.1109/tii.2019.2905295
  9. H. Yang, Q.-L. Han, X. Ge and et al.: Fault tolerant cooperative control of multi-agent systems: A survey of trends and methodologies. IEEE Transactions on Industrial Inform. 16 (2020), 4-17.   DOI:10.1109/tii.2019.2945004
  10. Y. Su and J. Huang: Cooperative output regulation of linear multi-agent systems. IEEE Trans. Automat. Control 57 (2011), 1062-1066.   DOI:10.1109/tac.2011.2169618
  11. Y. Su and J. Huang: Cooperative output regulation with application to multi-agent consensus under switching network. IEEE Trans. Cybernetics 42 (2012), 864-875.   DOI:10.1109/tsmcb.2011.2179981
  12. X. Ge and Q.-L. Han: Consensus of multiagent systems subject to partially accessible and overlapping Markovian network topologies. IEEE Trans. Cybernetics 47 (2017), 1807-1819.   DOI:10.1109/tcyb.2016.2570860
  13. H. Haghshenas, M. A. Badamchizadeh and M. Baradarannia: Containment control of heterogeneous linear multi-agent systems. Automatica 54 (2015), 210-216.   DOI:10.1016/j.automatica.2015.02.002
  14. Z. Li, M. Z. Chen and Z. Ding: Fully distributed adaptive controllers for cooperative output regulation of heterogeneous linear multi-agent systems with directed graphs. arXiv preprint arXiv:1411.7125 54 (2014).   CrossRef
  15. H. Cai and J. Huang: Cooperative output regulation with application to multi-agent consensus under switching network. IEEE Trans. Automat. Control 61 (2017), 3152-3157.   DOI:10.1109/tac.2014.2368231
  16. H. Cai, F. L. Lewis, G. Hu and J. Huang: The adaptive distributed observer approach to the cooperative output regulation of linear multi-agent systems. Automatica 75 (2017), 299-305.   DOI:10.1016/j.automatica.2016.09.038
  17. W. Liu and J. Huang: Adaptive leader-following consensus for a class of higher-order nonlinear multi-agent systems with directed switching networks. Automatica 75 (2017), 84-92.   DOI:10.1016/j.automatica.2017.02.010
  18. Y. Qian, L. Liu and G. Feng: Distributed Dynamic Event-Triggered Control for Cooperative Output Regulation of Linear Multiagent Systems. IEEE Trans. Cybernetics (2019), 1-10.   CrossRef
  19. X.-M. Zhang, Q.-L. Han, X. Ge and et al.: Networked control systems: A survey of trends and techniques. IEEE/CAA J. Automat. Sinica 7 (2020), 1-17.   DOI:10.1109/jas.2019.1911651
  20. L. Ding, Q.-L. Han, X. Ge and X.-M. Zhang: An overview of recent advances in event-triggered consensus of multiagent systems. IEEE transactions on cybernetics 48 (2017), 1110-1123.   DOI:10.1109/tcyb.2017.2771560
  21. D. V. Dimarogonas, E. Frazzoli and K. H. Johansson: Distributed event-triggered control for multi-agent systems. IEEE Trans. Automat. Control 57 (2011), 1291-1297.   DOI:10.1109/tac.2011.2174666
  22. Y. Fan, G. Feng, Y. Wang and C.Song: Distributed event-triggered control of multi-agent systems with combinational measurements. Automatica 49 (2013), 671-675.   DOI:10.1016/j.automatica.2012.11.010
  23. G. Guo, L. Ding and Q.-L. Han: A distributed event-triggered transmission strategy for sampled-data consensus of multi-agent systems. Automatica 50 (2014), 1489-1496.   DOI:10.1016/j.automatica.2014.03.017
  24. X. Ge, Q.-L. Han and F. Yang: Event-based set-membership leader-following consensus of networked multi-agent systems subject to limited communication resources and unknown-but-bounded noise. IEEE Trans. Industr. Electron. 64 (2016), 5045-5054.   DOI:10.1109/tie.2016.2613929
  25. G. S. Seyboth, D. V. Dimarogonas and K. H. Johansson: Event-based broadcasting for multi-agent average consensus. Automatica 49 (2013), 245-252.   DOI:10.1016/j.automatica.2012.08.042
  26. X. Meng and T. Chen: Event based agreement protocols for multi-agent networks. Automatica 49 (2013), 2125-2132.   DOI:10.1016/j.automatica.2013.03.002
  27. X. Ge, Q.-L. Han, X.-M. Zhang, L. Ding and F.Yang: Distributed event-triggered estimation over sensor networks: A survey. IEEE Trans. Cybernetics 50 (2019), 3, 1306-1320.   DOI:10.1109/tcyb.2019.2917179
  28. W. Hu and L. Liu: Cooperative output regulation of heterogeneous linear multi-agent systems by event-triggered control. IEEE Trans. Cybernet. 47 (2016), 105-116.   DOI:10.1109/tcyb.2015.2508561
  29. X. Wang, W. Ni and Z. Ma: Distributed event-triggered output regulation of multi-agent systems. Int. J. Control 88 (2015), 640-652.   DOI:10.1080/00207179.2014.971432
  30. W. Zou and Z. Xiang: Event-triggered distributed containment control of heterogeneous linear multi-agent systems by an output regulation approach. Int. J. Systems Sci. 48 (2017), 2041-2054.   DOI:10.1080/00207721.2017.1309595
  31. Y. Ma, Yajing and J. Zhao: Distributed integral-based event-triggered scheme for cooperative output regulation of switched multi-agent systems. Inform. Sci. 457 (2018), 208-221.   DOI:10.1016/j.ins.2018.02.021
  32. R. Yang, H. Zhang, G. Feng and H. Yan: Distributed event-triggered adaptive control for cooperative output regulation of heterogeneous multiagent systems under switching topology. IEEE Trans. Neural Networks Learning Systems 29 (2017), 4347-4358.   DOI:10.1109/tnnls.2017.2762343
  33. W. Liu and J. Huang: Event-triggered global robust output regulation for a class of nonlinear systems. IEEE Trans. Automat. Control 62 (2017), 5923-5930.   DOI:10.1109/tac.2017.2700384
  34. W. Liu and J. Huang: Cooperative global robust output regulation for a class of nonlinear multi-agent systems by distributed event-triggered control. Automatica 93 (2018), 138-148.   DOI:10.1016/j.automatica.2018.03.062
  35. Q. Yang, J. Sun and J. Chen: Output Consensus for Heterogeneous Linear Multiagent Systems With a Predictive Event-Triggered Mechanism. IEEE Trans. Cybernet. (2019), 1-13.   DOI:10.1109/tcyb.2019.2895044
  36. X. Meng, L. Xie and Y.C. Soh: Event-triggered output regulation of heterogeneous multiagent networks. IEEE Trans. Automat. Control 63 (2018), 4429-4434.   DOI:10.1109/tac.2018.2823085
  37. R. Yang, H. Zhang and G. Feng {et al.}: Robust cooperative output regulation of multi-agent systems via adaptive event-triggered control. Automatica 102 (2019), 129-136.   DOI:10.1016/j.automatica.2019.01.001
  38. W. Hu, L. Liu and G. Feng: Cooperative output regulation of linear multi-agent systems by intermittent communication: A unified framework of time-and event-triggering strategies. IEEE Trans. Automat. Control 63 (2017), 548-555.   DOI:10.1109/tac.2017.2727821
  39. X. Yi and, T. Yang and J. Wu: Distributed event-triggered control for global consensus of multi-agent systems with input saturation. Automatica 100 (2019), 1-9.   DOI:10.1016/j.automatica.2018.10.032
  40. Y. Su and J. Huang: Stability of a class of linear switching systems with applications to two consensus problems. IEEE Trans. Automat. Control 57 (2012), 1420-1430.   DOI:10.1109/tac.2011.2176391