Formation Control with Multiple Leaders via Event-triggering Transmission Strategy

  • Jing Liu
  • Jian-an FangEmail author
  • Zhen Li
  • Guang He


Event-triggering formation control with multiple leaders in second-order nonlinear multi-agent systems is investigated in this paper. This novel distributed formation control strategy allows the event-triggering condition to be intermittently examined at sampling instants, where the data transmission is driven by an event-triggering control protocol. Based on this strategy, two different formation control protocols are presented. Then, some sufficient conditions are given to ensure the second-order nonlinear multi-agent systems converge to the desired formation shape. Finally, examples are given to show the effectiveness of theoretical results.


Event-triggering protocol formation control multi-agent systems nonlinear dynamics. 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. Olfati-Saber, J. A. Fax, and R. M. Murray, “Consensus and cooperation in networked multi-agent systems,” Proceedings of the IEEE, vol. 95, no. 1, pp. 215–233, Jan 2007.CrossRefzbMATHGoogle Scholar
  2. [2]
    X. T. Wu, Y. Tang, J. D. Cao, and X. R. Mao, “Stability analysis for continuous-time switched systems with stochastic switching signals,” IEEE Transactions on Automatic Control, vol. 63, no. 9, pp. 3083–3090, Sep 2018.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    W. Zhang, Y. Tang, W. Huang, and J. Kurths, “Sampleddata consensus of linear multi-agent systems with packet losses,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 11, pp. 2516–2527, Nov 2016.CrossRefGoogle Scholar
  4. [4]
    Y. Liu, H. W. Chen, and J. Q. Lu, “Data-based controllability analysis of discrete-time linear time-delay systems,” International Journal of Systems Science, vol. 45, no. 11, pp. 2411–2417, 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    D. Huang, H. Jiang, Z. Yu, C. Kang, and C. Hu, “Leaderfollowing cluster consensus in multi-agent systems with intermittence,” International Journal of Control Automation and Systems, vol. 16, no. 9, pp. 1–15, Apr 2018.Google Scholar
  6. [6]
    Y. Tang, H. Gao, W. Zhang, and J. Kurths, “Leaderfollowing consensus of a class of stochastic delayed multiagent systems with partial mixed impulses,” Automatica, vol. 53, pp. 346–354, Mar 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    G.Wen, J. Huang, C.Wang, Z. Chen, and Z. Peng, “Group consensus control for heterogeneous multi-agent systems with fixed and switching topologies,” International Journal of Control, vol. 89, no. 2, pp. 259–269, Feb 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Y. Tang, X. Xing, H. R. Karimi, L. Kocarev, and J. Kurths, “Leader-following consensus of a class of stochastic delayed multi-agent systems with partial mixed impulses,” IEEE Transactions on Industrial Electronics, vol. 63, no. 2, pp. 1299–1307, Mar 2016.CrossRefGoogle Scholar
  9. [9]
    Y. Tang, D. Zhang, D. W. C. Ho, and F. Qian, “Tracking control of a class of cyber-physical systems via a FlexRay communication network,” IEEE Transactions on Cybernetics, vol. 49, no. 4, pp. 1186–1199, April 2019.CrossRefGoogle Scholar
  10. [10]
    Y. Zhang, G. Liu, and B. Luo, “Finite-time cascaded tracking control approach for mobile robots,” Information Sciences, vol. 284, no. 284, pp. 31–43, Nov 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    G. X. Wen, C. L. Philip Chen, and Y. J. Liu, “Formation control with obstacle avoidance for a class of stochastic multi-agent systems,” IEEE Transactions on Industrial Electronics, vol. 65, no. 7, pp. 5847–5855, July 2018.CrossRefGoogle Scholar
  12. [12]
    Y. Cao, D. Stuart, W. Ren, and Z. Meng, “Distributed containment control for multiple autonomous vehicles with double-integrator dynamics: algorithms andexperiments,” IEEE Transactions on Control Systems Technology, vol. 19, no. 4, pp. 929–938, July 2011.CrossRefGoogle Scholar
  13. [13]
    J. Han and Y. Q. Chen, “Multiple uav formations for cooperative source seeking and contour mapping of a radiative signal field,” Journal of Intelligent and Robotic Systems, vol. 74, no. 1–2, pp. 323–332, Apr 2014.CrossRefGoogle Scholar
  14. [14]
    N. Nigam, S. Bieniawski, I. Kroo, and J. Vian, “Control of multiple uavs for persistent surveillance: algorithm and flight test results,” IEEE Transactions on Control Systems Technology, vol. 20, no. 5, pp. 1236–1251, Sep 2012.CrossRefGoogle Scholar
  15. [15]
    S. Oh, L. Schenato, P. Chen, and S. Sastry, “Tracking and coordination of multiple agents using sensor networks: system design, algorithms and experiments,” Proceedings of the IEEE, vol. 95, no. 1, pp. 234–254, Jan 2007.CrossRefGoogle Scholar
  16. [16]
    J. L. Wang and H. N. Wu, “Leader-following formation control of multi-agent systems under fixed and switching topologies,” International Journal of Control, vol. 85, no. 6, pp. 695–705, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    X. Y. Luo, N. N. Han, and X. P. Guan, “Leader-following consensus protocols for formation control of multi-agent network,” Journal of Systems Engineering and Electronics, vol. 22, no. 6, pp. 991–997, Dec 2011.CrossRefGoogle Scholar
  18. [18]
    R. W. Beard, J. Lawton, and F. Y. Hadaegh, “A coordination architecture for spacecraft formation control,” IEEE Transactions on Control Systems Technology, vol. 9, no. 6, pp. 777–790, Nov 2001.CrossRefGoogle Scholar
  19. [19]
    J. A. Fax and R. M. Murray, “Information flow and cooperative control of vehicle formations,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1465–1476, Sep 2004.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    J. R. Lawton, R. W. Beard, and B. J. Young, “A decentralized approach to formation maneuvers,” IEEE Transactions on Robotics and Automation, vol. 19, no. 6, pp. 933–941, Dec 2003.CrossRefGoogle Scholar
  21. [21]
    X. H. Ge and Q. L. Han, “Distributed formation control of networked multi-agent systems using a dynamic eventtriggered communication mechanism,” IEEE Transactions on Industrial Electronics, vol. 64, no. 10, pp. 8118–8127, Oct 2017.CrossRefGoogle Scholar
  22. [22]
    P. Millan, L. Orihuela, I. Jurado, and F. R. Rubio, “Formation control of autonomous underwater vehicles subject to communication delays,” IEEE Transactions on Control Systems Technology, vol. 22, no. 2, pp. 770–777, Feb 2014.CrossRefGoogle Scholar
  23. [23]
    N. K. Mu, X. F. Liao, and T. W. Huang, “Leader-following consensus in second-order multiagent systems via eventtriggered control with nonperiodic sampled data,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 62, no. 10, pp. 1007–1011, Oct 2015.CrossRefGoogle Scholar
  24. [24]
    J. L. Liu, L. J. Zha, X. P. Xie, and E. G. Tian, “Resilient observer-based control for networked nonlinear T-S fuzzy systems with hybrid-triggered scheme,” Nonlinear Dynamics, vol. 91, no. 3, pp. 2049–2061, Feb 2018.CrossRefzbMATHGoogle Scholar
  25. [25]
    W. B. Zhang, Y. Tang, Y. R. Liu, and J. Kurths, “Eventtriggering containment control for a class of multi-agent networks with fixed and switching topologies,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 64, no. 3, pp. 619–629, Mar 2017.CrossRefGoogle Scholar
  26. [26]
    G. Guo, L. Ding, and Q. L. Han, “A distributed eventtriggered transmission strategy for sampled-data consensus of multi-agent systems,” Automatica, vol. 50, no. 5, pp. 1489–1496, May 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    W. Wang, C. Huang, J. D. Cao, and F. E. Alsaadi, “Eventtriggered control for sampled-data cluster formation of multi-agent systems,” Neurocomputing, vol. 267, pp. 25–35, Dec 2017.CrossRefGoogle Scholar
  28. [28]
    X. W. Dong and G. Q. Hu, “Time-varying formation control for general linear multi-agent systems with switching directed topologies,” Automatica, vol. 73, pp. 47–55, Nov 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    J. George and L. M. Kaplan, “A finite point process approach to multi-target localization using transient measurements,” Information Fusion, vol. 32, pp. 62–74, Nov 2016.CrossRefGoogle Scholar
  30. [30]
    Y. Li, H. Xiao, H. Wu, R. Hu, and Q. Fu, “Posterior cramercrao lower bounds for complicated multi-target tracking with labeled fisst based filters,” Signal Processing, vol. 127, pp. 156–167, Oct 2016.CrossRefGoogle Scholar
  31. [31]
    H. Tao, Z. H. Guan, C. Ming, B. Hu, L. Tao, and X. H. Zhang, “Multi-formation control of nonlinear leaderfollowing multi-agent systems,” ISA Transactions, vol. 69, pp. 140–147, July 2017.CrossRefGoogle Scholar
  32. [32]
    X. W. Dong, Q. D. Li, Q. L. Zhao, and Z. Ren, “Timevarying group formation analysis and design for secondorder multi-agent systems with directed topologies,” Neurocomputing, vol. 205, pp. 367–374, Sep 2016.CrossRefGoogle Scholar
  33. [33]
    X. W. Dong, Q. D. Li, Q. L. Zha, and Z. Ren, “Timevarying group formation analysis and design for general linear multi-agent systems with directed topologies,” International Journal of Robust and Nonlinear Control, vol. 27, no. 9, pp. 1640–1652, Jun 2017.MathSciNetzbMATHGoogle Scholar
  34. [34]
    Z. Li, J. A. Fang, T. W. Huang, and Q. Y. Miao, “Synchronization of stochastic discrete-time complex networks with partial mixed impulsive effects,” Journal of the Franklin Institute, vol. 354, no. 10, pp. 4196–4214, Jul 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    Z. Li, J. A. Fang, Q. Y. Miao, and G. He, “Exponential synchronization of impulsive discrete-time complex networks with time-varying delay,” Neurocomputing, vol. 157, no. 2, pp. 335–343, Jun 2015.CrossRefGoogle Scholar
  36. [36]
    L. J. Zha, J. A. Fang, J. L. Liu, and E. G. Tian, “Eventbased finite-time state estimation for markovian jump systems with quantizations and randomly occurring nonlinear perturbations,” ISA Transactions, vol. 66, pp. 77–85, Jan 2017.CrossRefGoogle Scholar
  37. [37]
    W. Yu, G. Chen, M. Cao, and J. Kurths, “Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 40, no. 3, pp. 881–891, Jun 2010.CrossRefGoogle Scholar
  38. [38]
    J. Qin, C. Yu, and B. D. O. Anderson, “On leaderless and leader-following consensus for interacting clusters of second-order multi-agent systems,” Automatica, vol. 74, pp. 214–221, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    W. Xia and M. Cao, “Clustering in diffusively coupled networks,” Automatica, vol. 47, no. 11, pp. 2395–2405, 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    J. Yu and L. Wang, “Group consensus in multi-agent systems with switching topologies and communication delays,” Systems & Control Letters, vol. 59, no. 6, pp. 340–348, Dec 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    H. Du, Y. Cheng, Y. He, and R. Jia, “Second-order consensus for nonlinear leader-following multi-agent systems via dynamic output feedback control,” International Journal of Robust and Nonlinear Control, vol. 26, no. 2, pp. 329–344, Jan 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  42. [42]
    D. Zheng, Linear System Theory, Tsinghua Univ. Press, Beijing, China, 2002.Google Scholar
  43. [43]
    W. Yu, G. Chen, and M. Cao, “Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems,” Automatica, vol. 46, no. 6, pp. 1089–1095, Jun 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    C. B. Yu, J. H. Qin, and H. J. Gao, “Cluster synchronization in directed networks of partial-state coupled linear systems under pinning control,” Automatica, vol. 50, no. 8, pp.2341–2349, Sep 2014.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.College of Information Science and TechnologyDonghua UniversityShanghaiChina
  2. 2.School of AutomationXi-an University of Posts & TelecommunicationsXi-an, ShannxiChina
  3. 3.Department of MathematicsAnhui Polytechnic UniversityWuhu, AnhuiChina

Personalised recommendations