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Consensus of Multi-agent Systems with Feedforward Nonlinear Dynamics and Digraph

  • Shuzhen Yu
  • Haijun Jiang
  • Zhiyong Yu
  • Cheng Hu
Regular Papers Control Theory and Applications
  • 53 Downloads

Abstract

This paper considers a high-order consensus problem of multi-agent system with feedforward nonlinear and time-varying input delay in a directed network. In order to achieve the consensus, we propose a low gain distributed protocol which can get rid of impacts of feedforward nonlinearity and an arbitrarily bounded input delay on the consensus problem. Moreover, for any upper bound time-varying delay and strongly connected diagraph, the proposed controller can solve the consensus problem of multi-agent systems with feedforward nonlinearity if the designed parameter θ is great than the threshold value. Finally, several numerical simulations are presented to demonstrate the validity of the theoretical results.

Keywords

Directed network feedforward high-order consensus input delay nonlinear multi-agent systems 

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References

  1. [1]
    J. Fax and R. Murray, “Information flow and cooperative control of vehicle formations,” IEEE Transactions on Automatic Control, vol. 35, no. 1, pp. 115–120, September 2002.Google Scholar
  2. [2]
    J. Cortés 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
  3. [3]
    F. Cucker and S. Smale, “Emergent behavior in flocks,” IEEE Transactions on Automatic Control, vol. 52, no. 5, pp. 852–862, May 2007.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    R. Olfati-Saber and R. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520–1533, September 2004.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    W. Ren and R. 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
  6. [6]
    Y. Sun, L. Wang, and G. Xie, “Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays,” Systems & Control Letters, vol. 57, no. 2, pp. 175–183, February 2008.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    J. Hu and J. Cao, “Hierarchical cooperative control for multiagent systems with switching directed topologies,” IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 10, pp. 2453–2463, January 2015.MathSciNetCrossRefGoogle Scholar
  8. [8]
    J. Lu, D. Ho, and J. Kurths, “Consensus over directed static networks with arbitrary finite communication delays,” Physical Review E Statistical Nonlinear & Soft Matter Physics, vol. 80, no. 2, pp. 066121, December 2009.CrossRefGoogle Scholar
  9. [9]
    W. Xu, D. Ho, L. Li, and J. Cao, “Event-triggered schemes on leader-following consensus of general linear multiagent systems under different topologies,” IEEE Transactions on Cybernetics, vol. 47, no. 1, pp. 212–223, January 2017.CrossRefGoogle Scholar
  10. [10]
    W. Ren and E. Atkins, “Distributed multi-vehicle coordinated control via local information exchang,” International Journal of Robust & Nonlinear Control, vol. 17, no. 10–11, pp. 1002–1033, July 2007.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    G. Xie and L. Wang, “Consensus control for a class of networks of dynamic agents: Fixed topology,” International Journal of Robust & Nonlinear Control, vol. 17, no. 10–11, pp. 941–959, July 2007.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    Y. Hong, G. Chen, and L. Bushnell, “Distributed observers design for leader-following control of multi-agent networks,” Automatica, vol. 44, no. 3, pp. 846–850, March 2008.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    Z. Ma, Z. Liu, and Z. Chen, “Modified leader-following consensus of time-delay multi-agent systems via sampled control and smart leader,” International Journal of Control, Automation and Systems, vol. 2, pp. 1–12, December 2017.Google Scholar
  14. [14]
    H. Hu, L. Yu, G. Chen, and G. Xie, “Second-order consensus of multi-agent systems with unknown but bounded disturbance,” International Journal of Control, Automation and Systems, vol. 11, no. 2, pp. 258–267, April 2013.CrossRefGoogle Scholar
  15. [15]
    Y. Tian and C. Liu, “Robust consensus of multi-agent systems with diverse input delays and asymmetric interconnection perturbations,” Automatica, vol. 45, no. 5, pp. 1347–1353, May 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    Z. Yu, H. Jiang, C. Hu, and X. Fan, “Consensus of secondorder multi-agent systems with delayed nonlinear dynamics and aperiodically intermittent communications,” International Journal of Control, vol. 90, no. 5, pp. 909–922, April 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    Q. Song, F. Liu, J. Cao, and W. Yu, “M-matrix strategies for pinning-controlled leader-following consensus in multiagent systems with nonlinear dynamics,” IEEE Transactions on Cybernetics, vol. 43, no. 6, pp. 1688–1697, December 2013.CrossRefGoogle Scholar
  18. [18]
    H. Wang, P. Liu, and P. Shi, “Observer-based fuzzy adaptive output-feedback control of stochastic nonlinear multiple time-delay systems,” IEEE Transactions on Cybernetics, vol. 47, no. 9, pp. 2568–2578, September 2017.CrossRefGoogle Scholar
  19. [19]
    X. Wang and H. Ji, “Leader-follower consensus for a class of nonlinear multi-agent systems,” International Journal of Control, Automation and Systems, vol. 10, no. 1, pp. 27–35, February 2012.CrossRefGoogle Scholar
  20. [20]
    Y. Cao, L. Zhang, C. Li, and M. Chen, “Observer-based consensus tracking of nonlinear agents in hybrid varying directed topology,” IEEE Transactions on Cybernetics, vol. 47, no. 8, pp. 2212–2222, August 2017.CrossRefGoogle Scholar
  21. [21]
    D. Meng and K. Moore, “Studies on resilient control through multiagent consensus networks subject to disturbances,” IEEE Transactions on Cybernetics, vol. 44, no. 11, pp. 2050–2064, November 2014.CrossRefGoogle Scholar
  22. [22]
    X. Zhao, H. Yang, H. Karimi, and Y. Zhu, “Adaptive neural control of MIMO nonstrict-feedback nonlinear systems with time delay,” IEEE Transactions on Cybernetics, vol. 46, no. 6, pp. 1337–1349, June 2016.CrossRefGoogle Scholar
  23. [23]
    H. Zhang, T. Feng, G. Yang, and H. Liang, “Distributed cooperative optimal control for multiagent systems on directed graphs: An inverse optimal approach,” IEEE Transactions on Cybernetics, vol. 45, no. 7, pp. 1315–1326, July 2015.CrossRefGoogle Scholar
  24. [24]
    X. Zhao, P. Shi, and X. Zheng, “Fuzzy adaptive control design and discretization for a class of nonlinear uncertain systems,” IEEE Transactions on Cybernetics, vol. 46, no. 6, pp. 1476–1483, June 2016.CrossRefGoogle Scholar
  25. [25]
    Y. Wang, J. Cao, and J. Hu, “Pinning consensus for multiagent systems with non-linear dynamics andtime-varying delay under directed switching topology,” IET Control Theory & Applications, vol. 8, no. 17, pp. 1931–1939, November 2014.CrossRefGoogle Scholar
  26. [26]
    H. Wang, X. Liu, and K. Liu, “Adaptive fuzzy tracking control for a class of pure-feedback stochastic nonlinear systems with non-lower triangular structure,” Fuzzy Sets and Systems, vol. 302, pp. 101–120, November 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    S. Neill and J. Cullen, “Experiments on whether schooling by their prey affects the hunting behaviour of cephalopods and fish predators,” Journal of Zoology, vol. 172, no. 4, pp. 549–569, April 1974.CrossRefGoogle Scholar
  28. [28]
    O. Schmitz, “Effects of predator hunting mode on grassland ecosystem function,” Ecology, vol. 90, no. 9, pp. 2339–2345, September 2009.CrossRefGoogle Scholar
  29. [29]
    T. Oksanen, L. Oksanen, and S. Fretwell, “Surplus killing in the hunting strategy of small predators,” The American Naturalist, vol. 126, no. 3, pp. 328–346, September 1985.CrossRefGoogle Scholar
  30. [30]
    A. Branscum, I. Gardner, and W. Johnson, “Bayesian modeling of animal- and herd-level prevalences,” Preventive Veterinary Medicine, vol. 66, no. 1–4, pp. 101–112, December 2004.CrossRefGoogle Scholar
  31. [31]
    P. Johnsen, T. Johannesson, and P. Sandøe, “Assessment of farm animal welfare at herd level: Many goals, many methods,” Acta Agriculturae Scandinavica, vol. 51, no. 1, pp. 26–33, February 2001.CrossRefGoogle Scholar
  32. [32]
    P. Lin, Y. Jia, J. Du, and S. Yuan, “Distributed consensus control for second-order agents with fixed topology and time-delay,” Proceedings of the 26th Chinese Control Conference, vol. 1986, no. 4, pp. 577–581, July 2007.Google Scholar
  33. [33]
    P. Lin and Y. 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
  34. [34]
    X. Liu, W. Lu, and T. Chen, “Consensus of multi-agent systems with unbounded time-varying delays,” IEEE Transactions on Automatic Control, vol. 55, no. 10, pp. 2396–2401, October 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    Y. Tian, and Y. Zhang, “High-order consensus of heterogeneous multi-agent systems with unknown communication delays,” Automatica, vol. 48, no. 6, pp. 1205–1212, June 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    S. Lee, “Consensus of feedforward nonlinear systems with a time-varying communication,” International Journal of Systems Science, vol. 48, no. 5, pp. 1106–1114, April 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    M. Koo and J. Lim, “Output feedback regulation of a chain of integrators with an unknown time-varying delay in the input,” IEEE Transactions on Automatic Control, vol. 55, no. 1, pp. 263–268, January 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  38. [38]
    F. Mazenc, S. Mondie, and R Francisco, “Global asymptotic stabilization of feedforward systems with delay in the input,” IEEE Transactions on Automatic Control, vol. 49, no. 5, pp. 844–850, May 2004.MathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    Y. Lim and H. Ahn, “Partial consensus of identical feedforward dynamic systems with input saturations,” International Journal of Robust & Nonlinear Control, vol. 26, no. 11, pp. 2494–2510, July 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    M. Koo and H. Choi, “Non-predictor control of a class of feedforward nonlinear systems with unknown time-varying delays,” International Journal of Control, vol. 89, no. 8, pp. 1–9, July 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    W. Yu, G. Chen, M. Cao, and J. Kurths, “Second-order consensus for multiagent systemsWith directed topologies and nonlinear dynamics,” IEEE Transactions on Systems Man & Cybernetics Part B: Cybernetics, vol. 40, no. 3, pp. 881–891, June 2010.CrossRefGoogle Scholar
  42. [42]
    A. Langville and W. Stewart, “The kronecker product and stochastic automata networks,” Journal of Computational & Applied Mathematics, vol. 167, no. 2, pp. 429–447, June 2004.MathSciNetCrossRefzbMATHGoogle Scholar
  43. [43]
    Z. Yu, H. Jiang, and C. Hu, “Second-order consensus for multi-agent systems via intermittent sampled data control,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, DOI: 10.1109/TSMC.2017.2687944.Google 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

  • Shuzhen Yu
    • 1
  • Haijun Jiang
    • 1
  • Zhiyong Yu
    • 1
  • Cheng Hu
    • 1
  1. 1.College of Mathematics and System SciencesXinjiang UniversityUrumqiP. R. China

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