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Adaptive consensus tracking of high-order nonlinear multi-agent systems with directed communication graphs

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  • Control Theory
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Abstract

This paper studies the adaptive consensus tracking problem for multi-agent systems modeled as high-order integrators with uncertain nonlinear dynamics under directed communication graphs. By parameterizing the unknown dynamics of the agents and the unknown input of the leader, two decentralized tracking control laws are designed using the state information and only the output information, respectively. With state information, globally uniformly ultimately bounded consensus tracking with arbitrarily small tracking errors can be achieved and when only output information is available, based on high-gain observers, semi-global result can be obtained. Numerical examples are provided to illustrate the effectiveness of the controllers.

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References

  1. W. Ren, R. Beard, and E. Atkins, “Information consensus in multivehicle cooperative control,” IEEE Control Systems Magazine, vol. 27, no. 2, pp. 71–82, 2007.

    Article  Google Scholar 

  2. R. Olfati-Saber, J. A. Fax, and R. M. Murray, “Consensus and cooperation in networked multiagent systems,” Proc. of the IEEE, vol. 95, pp. 215–233, 2007.

    Article  Google Scholar 

  3. W. Ren, “Second-order consensus algorithm with extensions to switching topologies and reference models,” Proc. of the American Control Conference, pp. 1431–1436, 2007.

    Google Scholar 

  4. Y. Hong, G. Chen, and L. Bushnell, “Distributed observers design for leader-following control of multiagent networks,” Automatica, vol. 44, no. 3, pp. 846–850, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  5. W. Ni and D. Cheng, “Leader-following consensus of multi-agent systems under fixed and switching topologies,” Systems & Control Letters, vol. 59, no. 3, pp. 209–217, 2010.

    Article  MATH  MathSciNet  Google Scholar 

  6. L. Gao, X. Zhu, and W. Chen, “Leader-following consensus problem with an accelerated motion leader,” International Journal of Control, Automation and Systems, vol. 10, no. 5, pp. 931–939, 2012.

    Article  Google Scholar 

  7. Z. Li, X. Liu, W. Ren, and L. Xie, “Distributed tracking control for linear multiagent systems with a leader of bounded unknown input,” IEEE Trans. on Automatic Control, vol. 58, no. 2, pp. 518–523, 2013.

    Article  MathSciNet  Google Scholar 

  8. X.-H. Wang and H.-B. 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, 2012.

    Article  MathSciNet  Google Scholar 

  9. Z. Li, W. Ren, X. Liu, and L. Xie, “Distributed consensus of linear multi-agent systems with adaptive dynamic protocols,” Automatica, vol. 49, no. 7, pp. 1986–1995, 2013.

    Article  MathSciNet  Google Scholar 

  10. H. Su, G. Chen, X. Wang, and Z. Lin, “Adaptive second-order consensus of networked mobile agents with nonlinear dynamics,” Automatica, vol. 47, no. 2, pp. 368–375, 2011.

    Article  MATH  MathSciNet  Google Scholar 

  11. G. Hu, “Robust consensus tracking for an integrator type multi-agent system with disturbances and unmodelled dynamics,” International Journal of Control, vol. 84, no. 1, pp. 1–8, 2011.

    Article  MATH  MathSciNet  Google Scholar 

  12. G. Hu, “Robust consensus tracking of a class of second-order multi-agent dynamic systems,” Systems & Control Letters, vol. 61, no. 1, pp. 134–142, 2012.

    Article  MATH  MathSciNet  Google Scholar 

  13. H. Zhang and F. L. Lewis, “Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics,” Automatica, vol. 48, no. 7, pp. 1432–1439, 2012.

    Article  MATH  MathSciNet  Google Scholar 

  14. H. Yu and X. Xia, “Adaptive consensus of multiagents in networks with jointly connected topologies,” Automatica, vol. 48, no. 8, pp. 1783–1790, 2012.

    Article  MATH  MathSciNet  Google Scholar 

  15. H. Liang, H. Zhang, Z. Wang, and J. Wang, “Output regulation of state-coupled linear multi-agent systems with globally reachable topologies,” Neurocomputing, vol. 123, pp. 337–343, 2014.

    Article  Google Scholar 

  16. H. Li, X. Liao, and G. Chen, “Leader-following finite-time consensus in second-order multi-agent networks with nonlinear dynamics,” International Journal of Control, Automation and Systems, vol. 11, no. 2, pp. 422–426, 2013.

    Article  Google Scholar 

  17. W. Yu, G. Chen, W. Ren, J. Kurths, and W. Zheng, “Distributed higher order consensus protocols in multiagent dynamical systems,” IEEE Trans. on Circuits and Systems I: Regular Papers, vol. 58, no. 8, pp. 1924–1932, 2011.

    Article  MathSciNet  Google Scholar 

  18. S. Tong and Y. Li, “Observer-based fuzzy adaptive control for strict-feedback nonlinear systems,” Fuzzy Sets and Systems, vol. 160, no. 12, pp. 1749–1764, 2009.

    Article  MATH  MathSciNet  Google Scholar 

  19. S.-C. Tong, X.-L. He, and H.-G. Zhang, “A combined backstepping and small-gain approach to robust adaptive fuzzy output feedback control,” IEEE Trans. on Fuzzy Systems, vol. 17, no. 5, pp. 1059–1069, 2009.

    Article  Google Scholar 

  20. S. Tong, C. Liu, and Y. Li, “Fuzzy-adaptive decentralized output-feedback control for large-scale nonlinear systems with dynamical uncertainties,” IEEE Trans. on Fuzzy Systems, vol. 18, no. 5, pp. 845–861, 2010.

    Article  Google Scholar 

  21. S. Tong, Y. Li, Y. Li, and Y. Liu, “Observer-based adaptive fuzzy backstepping control for a class of stochastic nonlinear strict-feedback systems,” IEEE Trans. on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 41, no. 6, pp. 1693–1704, 2011.

    Article  MathSciNet  Google Scholar 

  22. Y.-J. Liu, C. P. Chen, G.-X. Wen, and S. Tong, “Adaptive neural output feedback tracking control for a class of uncertain discrete-time nonlinear systems,” IEEE Trans. on Neural Networks, vol. 22, no. 7, pp. 1162–1167, 2011.

    Article  Google Scholar 

  23. G. Goodwin and K. Sin, Adaptive Filtering Prediction and Control, Dover Publications, 2009.

    MATH  Google Scholar 

  24. H. Bai, M. Arcak, and J. Wen, “Adaptive design for reference velocity recovery in motion coordination,” Systems & Control Letters, vol. 57, no. 8, pp. 602–610, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  25. H. Bai, M. Arcak, and J. Wen, “Adaptive motion coordination: using relative velocity feedback to track a reference velocity,” Automatica, vol. 45, no. 4, pp. 1020–1025, 2009.

    Article  MATH  MathSciNet  Google Scholar 

  26. H. K. Khalil, Nonlinear Systems, Prentice-Hall, Englewood Cliffs, 1996.

    Google Scholar 

  27. B. Aloliwi and H. K Khalil, “Robust adaptive output feedback control of nonlinear systems without persistence of excitation,” Automatica, vol. 33, no. 11, pp. 2025–2032, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  28. S. Seshagiri and H. Khalil, “Output feedback control of nonlinear systems using RBF neural networks,” IEEE Trans. on Neural Networks, vol. 11, no. 1, pp. 69–79, 2000.

    Article  Google Scholar 

  29. H. Zhang, D. Liu, Y. Luo, and D. Wang, Adaptive Dynamic Programming for Control: Algorithms and Stability, Springer, 2013.

    Book  Google Scholar 

  30. Z. Hou, L. Cheng, and M. Tan, “Decentralized robust adaptive control for the multiagent system consensus problem using neural networks,” IEEE Trans. on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 39, no. 3, pp. 636–647, 2009.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, 100871, China

    Junjie Fu & Jinzhi Wang

Authors
  1. Junjie Fu
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  2. Jinzhi Wang
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Correspondence to Jinzhi Wang.

Additional information

Junjie Fu received his B.S. degree in Theoretical and Applied Mechanics from Peking University in 2007. He is currently a Ph.D. Candidate in the State Key Laboratory for Turbulence and Complex System, Department of Mechanic and Engineering Science, Peking University, Beijing, China. His research interests include multi-agent systems and complex networks.

Jinzhi Wang received her M.S. degree in Mathematics from Northeast Normal University, China in 1988, and her Ph.D. degree in Control Theory from Peking University in 1998. From July 1998 to February 2000 she was a post-doctor at Institute of Systems Science, the Chinese Academy of Sciences. From March 2000 to August 2000 she was a research associate in the University of Hong Kong. She is currently a professor at the Department of Mechanics and Engineering Science, Peking University. Her research interests include robust control and control of nonlinear dynamical systems.

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Fu, J., Wang, J. Adaptive consensus tracking of high-order nonlinear multi-agent systems with directed communication graphs. Int. J. Control Autom. Syst. 12, 919–929 (2014). https://doi.org/10.1007/s12555-013-0325-0

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  • DOI: https://doi.org/10.1007/s12555-013-0325-0

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