Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Event-triggered encirclement control of multi-agent systems with bearing rigidity


In recent years, the problem of multi-agent encirclement has attained much attention and was extensively studied. However, few work consider the factor that the on-board calculation as well as the communication capacity in the multi-agent system is limited. We investigate the encirclement control by employing the newly developed bearing rigidity theory and event-triggered mechanism. Firstly, in order to reduce the onboard loads, the event-triggered mechanism is considered in the framework and further an event-triggered control law based on bearing rigidity is proposed. The input-to-state stability (ISS) of networked agents is also analyzed by using the Lyapunov method and the cyclic-small-gain theory. In addition, the lower bound for the inter-event times is provided. Finally, to verify the efficiency and feasibility of the proposed encirclement control law, numerical experiments are investigated.

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


  1. 1

    Haque M A. Biologically inspired heterogeneous multi-agent systems. Dissertation for Ph.D. Degree. Atlanta: Georgia Institute of Technology, 2010. 9–15

  2. 2

    Marshall J A, Broucke M E, Francis B A. Formations of vehicles in cyclic pursuit. IEEE Trans Autom Control, 2004, 49: 1963–1974

  3. 3

    Wang X, Zeng Z, Cong Y. Multi-agent distributed coordination control: developments and directions via graph viewpoint. Neurocomputing, 2016, 199: 204–218

  4. 4

    Ji M, Ferrari-Trecate G, Egerstedt M, et al. Containment control in mobile networks. IEEE Trans Autom Control, 2008, 53: 1972–1975

  5. 5

    Li Z, Ren W, Liu X, et al. Distributed containment control of multi-agent systems with general linear dynamics in the presence of multiple leaders. Int J Robust Nonlin Control, 2013, 23: 534–547

  6. 6

    Franchi A, Petitti A, Rizzo A. Decentralized parameter estimation and observation for cooperative mobile manipulation of an unknown load using noisy measurements. In: Proceedings of the 2015 IEEE International Conference on Robotics and Automation (ICRA), Seattle, 2015. 5517–5522

  7. 7

    Parrish J K, Viscido S V, Grunbaum D. Self-organized fish schools: an examination of emergent properties. Biol Bull, 2002, 202: 296–305

  8. 8

    Kim T H, Sugie T. Cooperative control for target-capturing task based on a cyclic pursuit strategy. Automatica, 2007, 43: 1426–1431

  9. 9

    Wen G, Duan Z, Chen G, et al. Consensus tracking of multi-agent systems with lipschitz-type node dynamics and switching topologies. IEEE Trans Circ Syst I Regul Pap, 2014, 61: 499–511

  10. 10

    Zheng R, Liu Y, Sun D. Enclosing a target by nonholonomic mobile robots with bearing-only measurements. Automatica, 2015, 53: 400–407

  11. 11

    Daingade S, Sinha A. Target centric cyclic pursuit using bearing angle measurements only. IFAC Proc Volume, 2014, 47: 491–496

  12. 12

    Zhao S, Zelazo D. Bearing rigidity and almost global bearing-only formation stabilization. IEEE Trans Autom Control, 2016, 61: 1255–1268

  13. 13

    Zhao S, Zelazo D. Localizability and distributed protocols for bearing-based network localization in arbitrary dimensions. Automatica, 2016, 69: 334–341

  14. 14

    Yu H, Antsaklis P J. Event-triggered real-time scheduling for stabilization of passive and output feedback passive systems. In: Proceedings of the 2011 American Control Conference, San Francisco, 2011. 1674–1679

  15. 15

    Li S, Xu B. Event-triggered control for discrete-time uncertain linear parameter-varying systems. In: Proceedings of the 32nd Chinese Control Conference, Xi’an, 2013. 273–278

  16. 16

    Lemmon M, Chantem T, Hu X S, et al. On self-triggered full-information h-infinity controllers. In: Proceedings of the 10th International Conference on Hybrid Systems: Computation and Control. Berlin: Springer, 2007. 371–384

  17. 17

    Dimarogonas D V, Frazzoli E, Johansson K H. Distributed event-triggered control for multi-agent systems. IEEE Trans Autom Control, 2012, 57: 1291–1297

  18. 18

    Fan Y, Feng G, Wang Y, et al. Distributed event-triggered control of multi-agent systems with combinational measurements. Automatica, 2013, 49: 671–675

  19. 19

    Mazo M, Tabuada P. Decentralized event-triggered control over wireless sensor/actuator networks. IEEE Trans Autom Control, 2011, 56: 2456–2461

  20. 20

    Tang T, Liu Z X, Chen Z Q. Event-triggered formation control of multi-agent systems. In: Proceedings of the 30th Chinese Control Conference, Yantai, 2011. 4783–4786

  21. 21

    Hu S, Yue D. Event-based h1 filtering for networked system with communication delay. Signal Process, 2012, 92: 2029–2039

  22. 22

    Yin X X, Yue D. Event-triggered tracking control for heterogeneous multi-agent systems with markov communication delays. J Franklin Inst, 2013, 350: 1312–1334

  23. 23

    Tallapragada P, Chopra N. On event triggered tracking for nonlinear systems. IEEE Trans Autom Control, 2013, 58: 2343–2348

  24. 24

    Liu T, Hill D J, Jiang Z P. Lyapunov formulation of ISS cyclic-small-gain in continuous-time dynamical networks. Automatica, 2011, 47: 2088–2093

  25. 25

    Dashkovskiy S N, Rüffer B S, Wirth F R. Small gain theorems for large scale systems and construction of iss Lyapunov functions. SIAM J Control Optimiz, 2010, 48: 4089–4118

  26. 26

    Wang X, Liu T, Qin J. Second-order consensus with unknown dynamics via cyclic-small-gain method. IET Control Theory Appl, 2012, 6: 2748–2756

  27. 27

    Sontag E D. Smooth stabilization implies coprime factorization. IEEE Trans Autom Control, 1989, 34: 435–443

  28. 28

    Jiang Z P, Mareels I M Y, Wang Y. A lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems. Automatica, 1996, 32: 1211–1215

Download references


This work was supported by National Natural Science Foundation of China (Grant Nos. 61473005, 61403406).

Author information

Correspondence to Xiangke Wang.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Yu, Y., Zeng, Z., Li, Z. et al. Event-triggered encirclement control of multi-agent systems with bearing rigidity. Sci. China Inf. Sci. 60, 110203 (2017).

Download citation


  • encirclement control
  • event-triggered
  • multi-agent system
  • bearing rigidity