A Novel Leader-following Consensus of Multi-agent Systems with Smart Leader

  • Fu-Yong Wang
  • Zhong-Xin LiuEmail author
  • Zeng-Qiang Chen
Regular Papers Control Theory and Applications


This article studies the leader-following consensus problem for mixed-order multi-agent systems with a leader. Different from the traditional leader which is independent of all the other agents, the leader, called smart leader, can obtain and utilize the feedback information from its neighbors at some disconnected time intervals. A new distributed consensus control protocol based on intermittent control is developed for leader-following consensus with a smart leader. Moreover, the smart leader can adjust the control protocol based on the feedback information from its neighbors. With the aid of Lyapunov function, some sufficient conditions are derived for leader-following consensus of multi-agent systems with mixed-order dynamics under fixed directed topology. In addition, the similar results are obtained under switching directed topology. Finally, simulation results are provided to verify the correctness and effectiveness of theoretical results.


Distributed control information feedback leader-following consensus mixed-order multi-agent systems smart leader 


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  1. [1]
    C. M. Topaz and A. L. Bertozzi, “Swarming patterns in a two-dimensional kinematic model for biological groups,” SIAM Journal on Applied Mathematics, vol. 65, no. 1, pp. 152–174, September 2004.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    I. D. Couzin, J. Krause, N. R. Franks, and S. A. Levin, “Effective leadership and decision-making in animal groups on the move,” Nature, vol. 433, no. 7025, pp. 513–516, February 2005.CrossRefGoogle Scholar
  3. [3]
    M. Nagy, Z. Akos, D. Biro, and T. Vicsek, “Hierarchical group dynamics in pigeon flocks,” Nature, vol. 464, no. 7290, pp. 890–893, April 2010.CrossRefGoogle Scholar
  4. [4]
    F. Giulietti, L. Pollini, and M. Innocenti, “Autonomous formation flight,” IEEE Control Systems, vol. 20, no. 6, pp. 34–44, December 2000.CrossRefGoogle Scholar
  5. [5]
    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, November 2001.CrossRefGoogle Scholar
  6. [6]
    A. Pant, P. Seiler, and K. Hedrick, “Mesh stability of lookahead interconnected systems,” IEEE Transactions on Automatic Control, vol. 47, no. 2, pp. 403–407, February 2002.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    R.W. Beard, T.W. McLain, M. A. Goodrich, and E. P. Anderson, “Coordinated target assignment and intercept for unmanned air vehicles,” IEEE Transactions on Robotics and Automation, vol. 18, no. 6, pp. 911–922, December 2002.CrossRefGoogle Scholar
  8. [8]
    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, September 2004.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    J. Cortes and F. Bullo, “Coordination and geometric optimization via distributed dynamical systems,” SIAM Journal on Control and Optimization, vol. 44, no. 5, pp. 1543–1574, November 2005.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    R. Olfati-Saber, “Flocking for multi-agent dynamic systems: algorithms and theory,” IEEE Transactions on Automatic Control, vol. 51, no. 3, pp. 401–420, March 2006.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    N. E. Leonard, D. A. Paley, F. Lekien, and R. E. Davis, “Collective motion, sensor networks, and ocean sampling,” Proceedings of the IEEE, vol. 95, no. 1, pp. 48–74, January 2007.CrossRefGoogle Scholar
  12. [12]
    H. T. Zhang, C. Zhai, and Z. Chen, “A general alignment repulsion algorithm for flocking of multi-agent systems,” IEEE Transactions on Automatic Control, vol. 56, no. 2, pp. 430–435, February 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    T. F. Liu and Z. P. Jiang, “Distributed formation control of nonholonomic mobile robots without global position measurements,” Automatica, vol. 49, no. 2, pp. 592–600, 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    Y. L. Wei, J. B. Qiu, H. R. Karimi, and M. Wang, “H¥ model reduction for continuous-time Markovian jump systems with incomplete statistics of mode information,” International Journal of Systems Science, vol. 45, no. 7, pp. 1496–1507, September 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    Y. L. Wei, J. B. Qiu, and H. R. Karimi, “Quantized H¥ filtering for continuous-time Markovian jump systems with deficient mode information,” Asian Journal of Control, vol. 17, no. 5, pp. 1914–1923, 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    Y. L. Wei, J. B. Qiu, H. K. Lam, and L. G. Wu, “Approaches to T-S fuzzy-affine-model-based reliable output feedback control for nonlinear It o stochastic systems,” IEEE Transactions on Circuits and Systems, vol. 25, no. 3, pp. 569–583, June 2017.Google Scholar
  17. [17]
    Y. L. Wei, J. B. Qiu, and H. R. Karimi, “Reliable output feedback control of discrete-time fuzzy affine systems with actuator faults,” IEEE Transactions on Fuzzy Systems, vol. 64, no. 1, pp. 170–181, January 2017.Google Scholar
  18. [18]
    X. Wang and G. H. Yang, “Adaptive reliable coordination control for linear agent networks with intermittent communication constraints,” IEEE Transactions on Control of Network Systems, DOI:10.1109/TCNS.2017.2687818.Google Scholar
  19. [19]
    W. Ren and R.W. Beard, “Consensus seeking in multiagent systems under dynamically changing interaction topologies,” IEEE Transactions on Automatic Control, vol. 50, no. 5, pp. 655–661, May 2005.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    P. Lin and Y. M. Jia, “Consensus of a class of second-order multi-agent systems with time-delay and jointly-connected topologies,” IEEE Transactions on Automatic Control, vol. 55, no. 3, pp. 778–784, March 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    Y. Z. Song, “Consensus of agents with mixed linear discrete dynamics,” International Journal of Control, Automation and Systems, vol. 14, no. 4, pp. 1139–1143, August 2016.CrossRefGoogle Scholar
  22. [22]
    J. Liu, P. Ming, and S. Li, “Consensus gain conditions of stochastic multi-agent system with communication noise,” International Journal of Control, Automation and Systems, vol. 14, no. 5, pp. 1223–1230, October 2016.CrossRefGoogle Scholar
  23. [23]
    J. H. Qin, H. J. Gao, T. Hayat, and F. E. Alsaadi, “Synchronising second-order multi-agent systems under dynamic topology via reference model-based algorithm,” Journal of Control and Decision, vol. 1, no. 3, pp. 214–225, 2014.CrossRefGoogle Scholar
  24. [24]
    X. Wang and G. H. Yang, “Distributed reliable consensus control for a class of multi-agent systems under switching networks: A topology-based average dwell time approach,” International Journal of Robust and Nonlinear Control, vol. 26, no. 13, pp. 2767–2787, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    Y. G. Hong, J. P. Hu, and L. X. 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
  26. [26]
    W. Zhu and D. Cheng, “Leader-following consensus of second-order agents with multiple time-varying delays,” Automatica, vol. 46, no. 12, pp. 1994–1999, 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    S. Djaidja and Q. H. Wu, “Leader-following consensus of single-integrator multi-agent systems under noisy and delayed communication,” International Journal of Control, Automation, and Systems, vol. 14, no. 2, pp. 357–366, April 2016.CrossRefGoogle Scholar
  28. [28]
    N. Huang, Z. S. Duan, and Y. Zhao, “Leader-following consensus of second-order non-linear multi-agent systems with directed intermittent communication,” IET Control Theory & Applications, vol. 8, no. 10, pp. 782–795, July 2014.MathSciNetCrossRefGoogle Scholar
  29. [29]
    A. H. Hu, J. D. Cao, and M. Hu, “Consensus of leaderfollowing multi-agent systems in time-varying networks via intermittent control,” International Journal of Control, Automation and Systems, vol. 12, no. 5, pp. 969–976, October 2014.CrossRefGoogle Scholar
  30. [30]
    E. Semsar-Kazerooni and K. Khorasani, “Optimal consensus algorithms for cooperative team of agents subject to partial information,” Automatica, vol. 44, no. 11, pp. 2766–2777, 2008.MathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    M.Wu, Y. He, and J. H. She, Stability Analysis and Robust Control of Time-delay Systems, Springer, Berlin, 2010.zbMATHGoogle Scholar
  32. [32]
    B. Boyd, L. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, 1994.CrossRefzbMATHGoogle Scholar
  33. [33]
    A. Olshevsky and J. N. Tsitsiklis, “On the nonexistence of quadratic Lyapunov functions for consensus algorithms,” IEEE Transactions on Automatic Control, vol. 53, no. 11, pp. 2642–2645, December 2008.MathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    G. H. Wen, Z. S. Duan, W. W Yu, and G. R. Chen, “Consensus in multi-agent systems with communication constraints,” International Journal of Robust and Nonlinear Control, vol. 22, no. 2, pp. 170–182, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    Z. H. Qu, Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles, Springer Science & Business Media, 2009.zbMATHGoogle Scholar
  36. [36]
    H. W. Zhang, F. L. Lewis, and Z. H. Qu, “Lyapunov, adaptive, and optimal design techniques for cooperative systems on directed communication graphs,” IEEE Transactions on Industrial Electronics, vol. 59, no. 7, pp. 3026–3041, July 2012.CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Computer and Control EngineeringNankai UniversityTianjinChina

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