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Adaptive leader-following rendezvous and flocking for a class of uncertain second-order nonlinear multi-agent systems

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Abstract

In this paper, we study the leader-following rendezvous and flocking problems for a class of second-order nonlinear multiagent systems, which contain both external disturbances and plant uncertainties. What differs our problems from the conventional leader-following consensus problem is that we need to preserve the connectivity of the communication graph instead of assuming the connectivity of the communication graph. By integrating the adaptive control technique, the distributed observer method and the potential function method, the two problems are both solved. Finally, we apply our results to a group of van der Pol oscillators.

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References

  1. A. Jadbabaie, J. Lin, A. S. Morse. Coordination of groups of mobile agents using nearest neighbor rules. IEEE Transactions on Automatic Control, 2003, 48(6): 988–1001.

    Article  MathSciNet  MATH  Google Scholar 

  2. R. Olfati-Saber, R. M. Murray. Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 2004, 49(9): 1520–1533.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Hu, Y. Hong. Leader-following coordination of multi-agent systems with coupling time delays. Physica A: Statistical Mechanics and its Applications, 2007, 374(2): 853–863.

    Article  Google Scholar 

  4. W. Ren. On consensus algorithms for double-integrator dynamics. IEEE Transactions on Automatic Control, 2008, 53(6): 1503–1509.

    Article  MathSciNet  MATH  Google Scholar 

  5. W. Liu, J. Huang. Adaptive leader-following consensus for a class of higher-order nonlinear multi-agent systems with directed switching networks. Automatica, 2017, 79: 84–92.

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Ji, M. Egerstedt. Distributed coordination control of multiagent systems while preserving connectedness. IEEE Transactions on Robotics, 2007, 23(4): 693–703.

    Article  Google Scholar 

  7. D. V. Dimarogonas, S. G. Loizou, K. J. Kyriakopoulos, et al. A feedback stabilization and collision avoidance scheme for multiple independent non-point agents. Automatica, 2006, 42(2): 229–243.

    Article  MathSciNet  MATH  Google Scholar 

  8. M. M. Zavlanos, G. J. Pappas. Potential fields for maintaining connectivity of mobile networks. IEEE Transactions on Robotics, 2007, 23(4): 812–816.

    Article  Google Scholar 

  9. M. M. Zavlanos, A. Jadbabaie, G. J. Pappas. Flocking while preserving network connectivity. Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans: IEEE, 2007: 2919–2924.

    Google Scholar 

  10. H. Su, X. Wang, G. Chen. Rendezvous of multiple mobile agents with preserved network connectivity. Systems & Control Letters, 2010, 59(5): 313–322.

    Article  MathSciNet  MATH  Google Scholar 

  11. Y. Dong, J. Huang. Flocking with connectivity preservation of multiple double integrator systems subject to external disturbances by a distributed control law. Automatica, 2015, 55: 197–203.

    Article  MathSciNet  MATH  Google Scholar 

  12. T. Gustavi, D. V. Dimarogonas, M. Egerstedt, et al. Sufficient conditions for connectivity maintenance and rendezvous in leader-follower networks. Automatica, 2010, 46(1): 133–139.

    Article  MathSciNet  MATH  Google Scholar 

  13. Y. Cao, W. Ren. Distributed coordinated tracking with reduced interaction via a variable structure approach. IEEE Transactions on Automatic Control, 2012, 57(1): 33–48.

    Article  MathSciNet  MATH  Google Scholar 

  14. H. Su, X. Wang, Z. Lin. Flocking of multi-agents with a virtual leader. IEEE Transactions on Automatic Control, 2009, 54(2): 293–307.

    Article  MathSciNet  MATH  Google Scholar 

  15. Y. Dong, J. Huang. A leader-following rendezvous problem of double integrator multi-agent systems. Automatica, 2013, 49(5): 1386–1391.

    Article  MathSciNet  MATH  Google Scholar 

  16. Y. Su. Leader-following rendezvous with connectivity preservation and disturbance rejection via internal model approach. Automatica, 2015, 57: 203–212.

    Article  MathSciNet  MATH  Google Scholar 

  17. Y. Dong, J. Huang. Leader-following consensus with connectivity preservation of uncertain Euler-lagrange multi-agent systems. Proceedings of the 53rd IEEE Conference on Decision and Control, Los Angeles: IEEE, 2014: 3011–3016.

    Chapter  Google Scholar 

  18. M. Wang, H. Su, M. Zhao, et al. Flocking of multiple autonomous agents with preserved network connectivity and heterogeneous nonlinear dynamics. Neurocomputing, 2013, 115: 169–177.

    Article  Google Scholar 

  19. Q. Zhang, P. Li, Z. Yang, et al. Adaptive flocking of non-linear multi-agents systems with uncertain parameters. IET Control Theory and Applications, 2015, 9(3): 351–357.

    Article  MathSciNet  Google Scholar 

  20. P. Yu, L. Ding, Z. Liu, et al. Leader-follower flocking based on distributed envent-triggered hybrid control. International Journal of Robust and Nonlinear Control, 2016, 26(1): 143–153.

    Article  MathSciNet  MATH  Google Scholar 

  21. W. Liu, J. Huang. Leader-following rendezvous and flocking for second-order nonlinear multi-agent systems. The 4th International Conference on Control, Decision and Information Technologies, Barcelona, Spain, 2017.

    Google Scholar 

  22. Y. Su, J. Huang. Cooperative output regulation of linear multiagent systems. IEEE Transactions on Automatic Control, 2012, 57(4): 1062–1066.

    Article  MathSciNet  MATH  Google Scholar 

  23. Z. Chen, J. Huang. Stabilization and Regulation of Nonlinear Systems: A Robust and Adaptive Approach. Switzerland: Springer, 2015.

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China

    Wei Liu & Jie Huang

Authors
  1. Wei Liu
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  2. Jie Huang
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Corresponding author

Correspondence to Jie Huang.

Additional information

This paper is dedicated to Professor T. J. Tarn on the occasion of his 80th birthday.

This work was supported by the Research Grants Council of the Hong Kong Special Administration Region (No. 14200515).

Wei LIU received the B.Eng. degree in 2009 from Southeast University, Nanjing, China, the M.Eng. degree in 2012 from University of Science and Technology of China, Hefei, China, and the Ph.D. degree in 2016 from The Chinese University of Hong Kong, Hong Kong, China. He is currently a Postdoctoral Fellow at The Chinese University of Hong Kong. His research interests include output regulation, event-triggered control, nonlinear control, multi-agent systems, and switched systems.

Jie HUANG is Choh-Ming Li professor and chairman of the Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong, China. His research interests include nonlinear control theory and applications, multi-agent systems, and flight guidance and control. Dr. Huang is a Fellow of IEEE, IFAC, CAA, and HKIE.

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Liu, W., Huang, J. Adaptive leader-following rendezvous and flocking for a class of uncertain second-order nonlinear multi-agent systems. Control Theory Technol. 15, 354–363 (2017). https://doi.org/10.1007/s11768-017-7083-0

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  • DOI: https://doi.org/10.1007/s11768-017-7083-0

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