Leader-following Formation Control of Second-order Nonlinear Systems with Time-varying Communication Delay

Abstract

In this paper, time-varying formation tracking problem for second-order nonlinear multi-agent systems with time-varying communication delays has been investigated, where the followers maintain a predefined time-varying formation while tracking the moving leader. Based on a distributed observer, a formation tracking protocol with time-varying delay is developed using the relative neighboring information. By constructing the Lyapunov-Krasovskii (L-K) function, sufficient conditions have been obtained to guarantee the stability of time-varying formation tracking. In addition, the unknown gain matrix in the proposed protocol is computed out through the technique of variable substitution. Numerical simulation results are presented to validate the effectiveness of our theoretical analysis.

This is a preview of subscription content, access via your institution.

References

  1. [1]

    Y. Lv, Q. Hu, G. Ma, and J. Zhang, “Attitude cooperative control of spacecraft formation via output-feedback,” Aircraft Engineering and Aerospace Technology, vol. 84, no. 5, pp. 321–329, 2012.

    Article  Google Scholar 

  2. [2]

    H. B. Duan and S. Q. Liu, “Non-linear dual-mode receding horizon control for multiple unmanned air vehicles formation flight based on chaotic particle swarm optimization,” IET Control Theory & Applications, vol. 4, no. 11, pp. 2565–2578, 2010.

    Article  Google Scholar 

  3. [3]

    H. K. Kim, H. B. Shim, and J. H. Back, “Formation control algorithm for coupled unicycle-type mobile robots through switching interconnection topology,” Journal of Institute of Control, Robotics and Systems (in Korean), vol. 18, no. 5, pp. 439–444, 2012.

    Article  Google Scholar 

  4. [4]

    Y. Wang, Y. Wei, X. Liu, N. Zhou, and C. G. Cassandras, “Optimal persistent monitoring using second-order agents with physical constraints,” IEEE Trans. on Automatic Control, vol. 64, no. 8, pp. 3239–3252, 2019.

    MathSciNet  MATH  Article  Google Scholar 

  5. [5]

    K. K. Oh, M. C. Park, and H. S. Ahn, “A survey of multiagent formation control,” Automatica, vol. 53, pp. 424–440, 2015.

    MathSciNet  MATH  Article  Google Scholar 

  6. [6]

    A. Mahmood and Y. Kim, “Leader-following formation control of quadcopters with heading synchronization,” Aerospace Science and Technology, vol. 47, pp. 68–74, 2015.

    Article  Google Scholar 

  7. [7]

    T. Balch and R. C. Arkin, “Behavior-based formation control for multirobot teams,” IEEE Trans. on robotics and automation, vol. 14, no. 6, pp. 926–939, 1998.

    Article  Google Scholar 

  8. [8]

    A. Sadowska, T. V. den Broek, H. Huijberts, N. van de Wouw, D. Kostić, and H. Nijmeijer, “A virtual structure approach to formation control of unicycle mobile robots using mutual coupling,” International Journal of Control, vol. 84, no. 11, pp. 1886–1902, 2011.

    MathSciNet  MATH  Article  Google Scholar 

  9. [9]

    W. Ren, “Consensus strategies for cooperative control of vehicle formations,” IET Control Theory & Applications, vol. 1, no. 2, pp. 505–512, 2007.

    Article  Google Scholar 

  10. [10]

    G. Xie and L. Wang, “Moving formation convergence of a group of mobile robots via decentralised information feedback,” International Journal of Systems Science, vol. 40, no. 10, pp. 1019–1027, 2009.

    MathSciNet  MATH  Article  Google Scholar 

  11. [11]

    X. Ge, Q. L. Han, and X. M. Zhang, “Achieving cluster formation of multi-agent systems under aperiodic sampling and communication delays,” IEEE Trans. on Industrial Electronics, vol. 65, no. 4, pp. 3417–3426, 2017.

    Article  Google Scholar 

  12. [12]

    Z. Lin, W. Ding, G. Yan, C. Yu and A. Giua, “Leader-follower formation via complex Laplacian,” Automatica, vol. 49, no. 6, pp. 1900–1906, 2013.

    MathSciNet  MATH  Article  Google Scholar 

  13. [13]

    J. Li and J. Li, “Adaptive iterative learning control for coordination of second-order multi-agent systems,” International Journal of Robust and Nonlinear Control, vol. 24, no. 18, pp. 3282–3299, 2014.

    MathSciNet  MATH  Article  Google Scholar 

  14. [14]

    Y. W. Wang, X. K. Liu, J. W. Xiao, and X. Lin, “Output formation-containment of coupled heterogeneous linear systems under intermittent communication,” Journal of the Franklin Institute, vol. 354, no. 1, pp. 392–414, 2017.

    MathSciNet  MATH  Article  Google Scholar 

  15. [15]

    H. Du, S. Li, and X. Lin, “Finite-time formation control of multiagent systems via dynamic output feedback,” International Journal of Robust and Nonlinear Control, vol. 23, no. 14, pp. 1609–28, 2013.

    MathSciNet  MATH  Article  Google Scholar 

  16. [16]

    S. Djaidja, Q. H. Wu, and H. Fang, “Leader-following consensus of double-integrator multi-agent systems with noisy measurements,” International Journal of Control Automation and Systems, vol. 13 no. 1, pp. 17–24, 2015.

    Article  Google Scholar 

  17. [17]

    J. Liu, J. Fang, Z. Li, and G. He, “Time-varying formation tracking for second-order multi-agent systems subjected to switching topology and input saturation,” International Journal of Control Automation and Systems, vol. 18, no. 4, pp. 991–1001, 2020.

    Article  Google Scholar 

  18. [18]

    Z. Lin, L. Wang, Z. Han, and M. Fu, “A Graph Laplacian Approach to Coordinate-Free Formation Stabilization for Directed Networks,” IEEE Trans. on Automatic Control, vol. 61, no. 5, pp. 1269–1280, 2016.

    MathSciNet  MATH  Article  Google Scholar 

  19. [19]

    J. Huang, G. Wen, Z. Peng, X. Chu, and Y. Dong, Y “Group-consensus with reference states for heterogeneous multiagent systems via pinning control,” International Journal of Control, Automation and Systems, vol. 17, no. 5, pp. 1096–1106, 2019.

    Article  Google Scholar 

  20. [20]

    S. Sastry, Nonlinear Systems: Analysis, Stability, and Control, Springer-Verlag, NewYork, 1999.

    Google Scholar 

  21. [21]

    J. Yu, X. Dong, Q. Li, and Z. Ren, “Practical time-varying formation tracking for second-order nonlinear multiagent systems with multiple leaders using adaptive neural networks,” IEEE Trans. on Neural Networks and Learning Systems, vol. 29, no. 12, pp. 6015–6025, 2018.

    MathSciNet  Article  Google Scholar 

  22. [22]

    D. Meng, Y. Jia, J. Du, and J. Zhang, “On iterative learning algorithms for the formation control of nonlinear multiagent systems,” Automatica, vol. 50, no. 1, pp. 291–295, 2014.

    MathSciNet  MATH  Article  Google Scholar 

  23. [23]

    T. Han, Z. H. Guan, M. Chi, B. Hu, T. Li, and X. H. Zhang, “Multi-formation control of nonlinear leader following multi agent systems,” ISA Transactions, vol. 69, pp. 140–147, 2017.

    Article  Google Scholar 

  24. [24]

    W. Li, Z. Chen, and Z. Liu, “Leader-following formation control for second-order multiagent systems with time-varying delay and nonlinear dynamics,” Nonlinear Dynamics, vol. 72, no. 4, pp. 803–812, 2013.

    MathSciNet  MATH  Article  Google Scholar 

  25. [25]

    G. Wen, Z. Peng, A. Rahmani, and Y. Yu, “Distributed leader-following consensus for second-order multi-agent systems with nonlinear inherent dynamics,” International Journal of Systems Science, vol. 45, no. 9, pp. 1892–1901, 2014.

    MathSciNet  MATH  Article  Google Scholar 

  26. [26]

    K. Subramanian, P. Muthukumar, and Y. H. Joo, “Leader-following consensus of nonlinear multi-agent systems via reliable control with time-varying communication delay,” International Journal of Control, Automation and Systems, vol. 17, no. 2, pp. 298–306, 2019.

    Article  Google Scholar 

  27. [27]

    D. Zhang, Q. Song, Y. Liu, and J. Cao, “Pinning consensus analysis for nonlinear second-order multi-agent systems with time-varying delays,” Asian Journal of Control, vol. 20 no. 6, pp. 2343–2350, 2018.

    MathSciNet  MATH  Article  Google Scholar 

  28. [28]

    J. Huang, G. Wen, Z. Peng, and Y. Zhang, “Cluster-delay consensus for second-order nonlinear multi-agent systems,” Journal of Systems Science and Complexity, vol. 33, pp. 333–344, 2020.

    MathSciNet  MATH  Article  Google Scholar 

  29. [29]

    X. Dong and G. Hu, “Time-varying formation tracking for linear multiagent systems with multiple leaders,” IEEE Trans. on Automatic Control, vol. 62, no.7, pp. 3658–3664, 2017.

    MathSciNet  MATH  Article  Google Scholar 

  30. [30]

    L. Han, X. Dong, Q. Li, and Z. Ren, “Formation tracking control for time-delayed multi-agent systems with second-order dynamics,” Chinese Journal of Aeronautics, vol. 30, no. 1, pp. 348–357, 2017.

    Article  Google Scholar 

  31. [31]

    T. Li, Z. Li, H. Zhang, and S. Fei, “Formation tracking control of second-order multi-agent systems with time-varying delay,” Journal of Dynamic Systems, Measurement, and Control, vol. 140, no. 11, 111015, 2018.

    Article  Google Scholar 

  32. [32]

    X. Dong, Y. Zhou, Z. Ren, and Y. Zhong, “Time-varying formation tracking for second-order multi-agent systems subjected to switching topologies with application to quadrotor formation flying,” IEEE Trans. on Industrial Electronics, vol. 64, no. 6, pp. 5014–5024, 2016.

    Article  Google Scholar 

  33. [33]

    W. Qin, Z. Liu, and Z. Chen, “A novel observer-based formation for nonlinear multi-agent systems with time delay and intermittent communication,” Nonlinear Dynamics, vol. 79, no. 3, pp. 1651–1664, 2015.

    MathSciNet  MATH  Article  Google Scholar 

  34. [34]

    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, 2008.

    MathSciNet  MATH  Article  Google Scholar 

  35. [35]

    F. Y. Wang, Z. X. Liu, and Z. Q. Chen, “A novel leader-following consensus of multi-agent systems with smart leader,” International Journal of Control Automation and Systems, vol. 16, no. 4, pp. 1483–1492, 2018.

    Article  Google Scholar 

  36. [36]

    J. Wang, Q. Li, and Z. Ren, “Observer-based finite-time coordinated tracking for general linear multi-agent systems,” Automatica, vol. 66, no. 66, pp. 231–237, 2016.

    MathSciNet  Google Scholar 

  37. [37]

    Y. Hua, X. Dong, J. Wang, Q. Li, and Z. Ren, “Time-varying output formation tracking of heterogeneous linear multi-agent systems with multiple leaders and switching topologies,” Journal of the Franklin Institute, vol. 356, no. 1, pp. 539–560, 2019.

    MathSciNet  MATH  Article  Google Scholar 

  38. [38]

    M. P. Ran, L. H. Xie, and J. C. Li, “Time-varying formation tracking for uncertain second-order nonlinear multiagent systems, ” Frontiers of Information Technology & Electronic Engineering, vol. 20, no. 1, pp. 76–87, 2019.

    Article  Google Scholar 

  39. [39]

    W. Yu, G. Chen, M. Cao and J. Kurths, “Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics,” Systems Man and Cybernetics, vol. 40, no. 3, pp. 881–891, 2010.

    Article  Google Scholar 

  40. [40]

    M. Wu, Y. He and J. H. She, Stability Analysis and Robust Control of Time-delay Systems, vol. 22, Springer, Berlin, 2010.

    Google Scholar 

  41. [41]

    O. M. Kwon, M. J. Park, J. H. Park, S. M. Lee, and E. J. Cha, “On stability analysis for neural networks with interval time-varying delays via some new augmented Lyapunov-Krasovskii functional,” Commnications in Nonlinear Science and Numerical Simulation, vol. 19, no. 9, pp. 3184–3201, 2014.

    MathSciNet  MATH  Article  Google Scholar 

  42. [42]

    X. Zhang, M. Wu, J. H. She, and Y. He, “Delay-dependent stabilization of linear systems with time-varying state and input delays,” Automatica, vol. 41, no. 8, pp. 1405–1412, 2005.

    MathSciNet  MATH  Article  Google Scholar 

  43. [43]

    Z. Li, G. Wen, Z. Duan, and W. Ren, “Designing fully distributed consensus protocols for linear multi-agent systems with directed graphs,” IEEE Trans. on Automatic Control, vol. 60, no. 4, pp. 1152–1157, 2014.

    MathSciNet  MATH  Article  Google Scholar 

  44. [44]

    S. J. Yoo and T. H. Kim, “Distributed formation tracking of networked mobile robots under unknown slippage effects,” Automatica, vol. 54, no. 54, pp. 100–106, 2015.

    MathSciNet  MATH  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Ming Wang.

Additional information

Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Muhammad Rehan under the direction of Editor Myo Taeg Lim.

Ming Wang received his B.S. degree in aircraft design and engineering from Xi’an Jiaotong University in 2017. He is currently working toward the Ph.D. degree in the University of Chinese Academy of Sciences, Beijing, where he majors in technology of computer. His research interests include nonlinear system control, reinforcement learning and multi-agent systems.

Tao Zhang received his B.S. and Ph.D. degrees in power engineering and control from Tsinghua University, Beijing, China, in 1995 and 2000, respectively. He is a Researcher and the Director of Department and Division, Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences, Beijing. His research interests include testing and verification technology for high reliability software, analysis and design method for high reliability electronic information system, simulation of complex system, the overall design of the space application system, and virtual reality technique.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Wang, M., Zhang, T. Leader-following Formation Control of Second-order Nonlinear Systems with Time-varying Communication Delay. Int. J. Control Autom. Syst. (2021). https://doi.org/10.1007/s12555-019-0759-0

Download citation

Keywords

  • Distributed observer
  • formation tracking control
  • linear matrix inequality
  • second-order nonlinear system
  • time-varying delay