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Flocking of Multi-agent Systems with Unknown Nonlinear Dynamics and Heterogeneous Virtual Leader

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  • Control Theory and Applications
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Abstract

This paper investigates the flocking control of multi-agent systems with unknown nonlinear dynamics while the virtual leader information is heterogeneous. The uncertain nonlinearity in the virtual leader information is considered, and the weaker constraint on the velocity information measurements is assumed. In addition, a bounded assumption on the unknown nonlinear dynamics is also considered. It is weaker than the Lipschitz condition adopted in the most flocking control methods. To avoid fragmentation, we construct a new potential function based on the penalty idea when the initial network is disconnected. A dynamical control law including a adjust parameter is designed to achieve the stable flocking. It is proven that the velocities of all agents approach to consensus and no collision happens between the mobile agents. Finally, several simulations verify the effectiveness of the new design, and indicate that the proposed method has high convergence and the broader applicability in practical applications with more stringent restrictions.

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References

  1. X. Xie and X. Mu, “Observer-based intermittent consensus control of nonlinear singular multi-agent systems,” International Journal of Control, Automation, and Systems, vol. 17, no. 9, pp. 2321–2330, September 2019.

    Article  Google Scholar 

  2. Y. Liu and G. Yang, “Distributed fixed-time consensus for multiagent systems with unknown control directions,” International Journal of Robust and Nonlinear Control, vol. 29, no. 11, pp. 3311–3329, July 2019.

    Article  MathSciNet  Google Scholar 

  3. 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, February 2011.

    Article  MathSciNet  Google Scholar 

  4. M. Chen and X. Wang, “Flocking dynamics for multi-agent system with measurement delay,” Mathematics and Computers in Simulation, vol. 171, pp. 187–200, May 2020.

    Article  MathSciNet  Google Scholar 

  5. G. Jing and L. Wang, “Multi-agent flocking with angle-based formation shape control,” IEEE Trans. on Automatic Control, vol. 65, no. 2, pp. 817–823, February 2020.

    Article  MathSciNet  Google Scholar 

  6. X. Luo, X. Li, S. Li, Z. Jiang, and X. Guan, “Flocking for multi-agent systems with optimally rigid topology based on information weighted Kalman,” International Journal of Control, Automation, and Systems, vol. 15, no. 1, pp. 138–148, February 2017.

    Article  Google Scholar 

  7. C. W. Reynolds, “Flocks, herds, and schools: A distributed behavioral model,” Computer Graphics, vol. 21, no. 4, pp. 25–34, July 1987.

    Article  Google Scholar 

  8. H. G. Tanner, A. Jadbabaie, and G. J. Pappas, “Stable flocking of mobile agents part II: Dynamic topology,” Proc. of 42nd IEEE Conference on Decision and Control, pp. 2016–2021, December 2003.

  9. R. Olfati-Saber, “Flocking for multi-agent dynamic systems: Algorithms and theory,” IEEE Trans. on Automatic Control, vol. 51, no. 3, pp. 401–420, March 2006.

    Article  MathSciNet  Google Scholar 

  10. H. G. Tanner, A. Jadbabaie, and G. J. Pappas, “Flocking in fixed and switching networks,” IEEE Trans. on Automatic Control, vol. 52, no. 5, pp. 863–868, May 2007.

    Article  MathSciNet  Google Scholar 

  11. J. Zhang, Y. Wang, J. Xiao, and Y. Shen, “Stability analysis of switched positive linear systems with stable and unstable subsystems,” International Journal of Systems Science, vol. 45, no. 12, pp. 2458–2465, December 2014.

    Article  MathSciNet  Google Scholar 

  12. X. Wang and G. Yang, “Fault-tolerant consensus tracking control for linear multiagent systems under switching directed network,” IEEE Trans. on Cybernetics, vol. 50, no. 5, pp. 1921–1930, May 2020.

    Article  Google Scholar 

  13. M. M. Zavlanos, A. Jadbabaie, and G. J. Pappas, “Flocking while preserving network connectivity,” Proc. of 46th IEEE Conference on Decision and Control, pp. 2919–1279, December 2007.

  14. H. Su, X. Wang, and G. Chen, “A connectivity-preserving flocking algorithm for multi-agent systems based only on position measurements,” International Journal of Control, vol. 82, no. 7, pp. 1334–1343, July 2009.

    Article  MathSciNet  Google Scholar 

  15. S. Su and Z. Lin, “Connectivity enhancing coordinated tracking control of multi-agent systems with a state-dependent jointly-connected dynamic interaction topology,” Automatica, vol. 101, pp. 431–438, March 2019.

    Article  MathSciNet  Google Scholar 

  16. J. Gao, X. Xu, N. Ding, and Q. E. Li, “Flocking motion of multi-agent system by dynamic pinning control,” IET Control Theory & Applications, vol. 11, no. 5, pp. 714–722, January 2017.

    Article  MathSciNet  Google Scholar 

  17. F. Sun, R. Wang, W. Zhu, and Y. Li, “Flocking in nonlinear multi-agent systems with time-varying delay via event-triggered control,” Applied Mathematics and Computation, vol. 350, pp. 66–77, June 2019.

    Article  MathSciNet  Google Scholar 

  18. Q. Zhang, Z. Gong, Z. Yang, and Z. Chen, “Distributed convex optimization for flocking of nonlinear multi-agent systems,” International Journal of Control, Automation, and Systems, vol. 17, no. 5, pp. 1177–1183, May 2019.

    Article  Google Scholar 

  19. Z. Peng, D. Wang, H. H. T. Liu, and G. Sun, “Neural adaptive control for leader-follower flocking of networked non-holonomic agents with unknown nonlinear dynamics,” International Journal of Adaptive Control and Signal Processing, vol. 28, no. 6, pp. 479–495, June 2014.

    Article  MathSciNet  Google Scholar 

  20. G. Wen, C. L. P. Chen, Y. Liu, and Z. Liu, “Neural network-based adaptive leader-following consensus control for a class of nonlinear multiagent state-delay systems,” IEEE Trans. on Cybernetics, vol. 47, no. 8, pp. 2151–2160, August 2016.

    Article  Google Scholar 

  21. B. Ning, Q. Han, Z. Zuo, J. Jin, and J. Zheng, “Collective behaviors of mobile robots beyond the nearest neighbor rules with switching topology,” IEEE Trans. on Cybernetics, vol. 48, no. 5, pp. 1577–1590, May 2018.

    Article  Google Scholar 

  22. Z. Yang, Q. Zhang, and Z. Chen, “Adaptive distributed convex optimization for multi-agent and its application in flocking behavior,” Journal of the Franklin Institute, vol 356, no. 2, pp. 1038–1050, January 2019.

    Article  MathSciNet  Google Scholar 

  23. Z. Yang, Q. Zhang, and Z. Chen, “Flocking of multi-agents with nonlinear inner-coupling functions,” Nonlinear Dynamics, vol. 60, no. 3, pp. 255–264, May 2010.

    Article  MathSciNet  Google Scholar 

  24. H. Atrianfar and M. Haeri, “Adaptive flocking control of nonlinear multi-agent systems with directed switching topologies and saturation constraints,” Journal of the Franklin Institute, vol. 350, no. 6, pp. 1545–1561, August 2013.

    Article  MathSciNet  Google Scholar 

  25. G. Wen, Z. Duan, Z. Li, and G. Chen, “Flocking of multiagent dynamical systems with intermittent nonlinear velocity measurements,” International Journal of Robust and Nonlinear Control, vol. 22, no. 16, pp. 1790–1805, November 2012.

    Article  MathSciNet  Google Scholar 

  26. H. G. Tanner, A. Jadbabaie, and G. J. Pappas, “Stable flocking of mobile agents, Part I: Fixed topology,” Proc. of 42nd IEEE Conference on Decision and Control, pp. 2010–2015, December 2003.

  27. J. Li, X. Chen, F. Hao, and J. Xie, “Event-triggered bipartite consensus for multi-agent systems with antagonistic interactions,” International Journal of Control, Automation, and Systems, vol. 17, no. 8, pp. 2046–2058, August 2019.

    Article  Google Scholar 

  28. M. Fan, H. Zhang, and M. Wang, “Bipartite flocking for multi-agent systems,” Communications in Nonlinear Science & Numerical Simulation, vol. 19, no. 9, pp. 3313–3322, September 2014.

    Article  MathSciNet  Google Scholar 

  29. K. Eliker and W. Zhang, “Finite-time adaptive integral backstepping fast terminal sliding mode control application on quadrotor UAV,” International Journal of Control, Automation, and Systems, vol. 18, no. 2, pp. 415–430, February 2020.

    Article  Google Scholar 

  30. M. G. Michailidis, M. J. Rutherford, and K. P. Valavanis, “A survey of controller designs for new generation UAVs: The challenge of uncertain aerodynamic parameters,” International Journal of Control, Automation, and Systems, vol. 18, no. 4, pp. 801–816, April 2020.

    Article  Google Scholar 

  31. H. K. Khalil and J. Grizzle, Nonlinear Systems, vol. 3, Prentice Hall, Upper Saddle River, NJ, 2002.

    Google Scholar 

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Authors and Affiliations

  1. College of Mathematics, Jilin University, 2699 Qianjin Street, Changchun, 130012, P. R. China

    Tingruo Yan, Xu Xu & Zongying Li

  2. School of Science, Engineering & Design, Teesside University, Middleborough, UK

    Eric Li

Authors
  1. Tingruo Yan
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  2. Xu Xu
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  3. Zongying Li
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  4. Eric Li
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Corresponding author

Correspondence to Xu Xu.

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This work was supported by the National Natural Scientific Foundation of China (NSFC) under grant number 12072128, the Special Funds of Provincial Industrial Innovation of Jilin Province China (No. 2017C028-1), and the Project of Science and Technology Development of Jilin Province China (No. 20190201302JC).

Tingruo Yan is a Ph.D. candidate at Jilin University, and his research topics are multi-agent systems and optimization.

Xu Xu is a professor at Jilin University. His research topics include computational intelligence, machine learning, and optimization. He obtained his Ph.D. degree from Jilin University in 2003. Currently, he is an editor of International Journal of Bifurcation and Chaos.

Zongying Li is a Ph.D. candidate at Jilin University, and now her research topic is about the optimization of complex network.

Eric Li is a senior lecturer in Teesside University, and his main research topics include machine learning and computational mechanics. He obtained his Ph.D. degree from National University of Singapore in 2012. Currently, he is an associate editor of International Journal of Computational Methods.

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Yan, T., Xu, X., Li, Z. et al. Flocking of Multi-agent Systems with Unknown Nonlinear Dynamics and Heterogeneous Virtual Leader. Int. J. Control Autom. Syst. 19, 2931–2939 (2021). https://doi.org/10.1007/s12555-020-0578-3

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  • DOI: https://doi.org/10.1007/s12555-020-0578-3

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