Skip to main content
SpringerLink
Log in

Fixed-time Consensus Tracking for Second-order Leader-follower Multi-agent Systems with Nonlinear Dynamics Under Directed Topology

  • Regular Papers
  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

In this paper, we address the fixed-time consensus tracking problem of second-order leader-follower multi-agent systems with nonlinear dynamics under directed topology. The consensus tracking algorithm consists of distributed observer and observer-based decentralized controller. The fixed-time distributed observer guarantees that each follower estimates the leader’s state under directed topology within a fixed time, where the upper bound of convergence time is independent on the initial conditions. The fixed-time decentralized controller makes each follower converge to the leader’s state in fixed time via tracking the distributed observer’s state and overcome the nonlinear dynamics without adding linear control terms. Finally, the numerical example is provided to illustrate the effectiveness of the results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Y.-J. Hong, J.-P. Hu, and L.-X. Gao, “Tracking control for multi-agent consensus with an active leader and variable topology,” Automatica, vol. 42, no. 7, pp. 1177–1182, 2006.

    Article  MathSciNet  Google Scholar 

  2. X.-C. Shi, J.-W. Lu, Z. Li, and S.-Y. Xu, “Robust adaptive distributed dynamic surface consensus tracking control for nonlinear multi-agent systems with dynamic uncertainties,” Journal of the Franklin Institute, vol. 353, no. 17, pp. 4785–4802, November 2016.

    Article  MathSciNet  Google Scholar 

  3. W.-T. Zhang, Y. Liu, J.-Q. Lu, and J.-D. Cao, “A novel consensus algorithm for second-order multi-agent systems without velocity measurements,” International Journal of Robust and Nonlinear Control, vol. 27, no. 15, pp. 2510–2528, October 2017.

    Article  MathSciNet  Google Scholar 

  4. D.-M. Xie, L. Shi, and F.-C. Jiang, “Group tracking control of second-order multi-agent systems with fixed and Markovian switching topologies,” Neurocomputing, vol. 281, pp. 37–46, March 2018.

    Article  Google Scholar 

  5. J.-H. Qin, G.-S. Zhang, W.-X. Zheng, and Y. Kang, “Adaptive sliding mode consensus tracking for second-order nonlinear multiagent systems with actuator faults,” IEEE Transactions on Cybernetics, vol. 49, no. 5, pp. 1605–1615, May 2019.

    Article  Google Scholar 

  6. J. Cheng, J.-H. Park, J.-D. Cao, and W.-H. Qi, “A hidden mode observation approach to finite-time SOFC of Markovian switching systems with quantization,” Nonlinear Dynamics, vol. 100, no. 1, pp. 509–521, March 2020.

    Article  Google Scholar 

  7. Y. Zhao, Y.-F. Liu, G.-H. Wen, N.D. Alotaibi, and Z.-K. Shi, “Distributed finite-time tracking of second-order multi-agent systems: An edge-based approach,” IET Control Theory and Applications, vol. 12, no. 1, pp. 149–154, January 2018.

    Article  MathSciNet  Google Scholar 

  8. D.-D. Zhang and G.-R. Duan, “Rotating consensus tracking for second-order multi-agent systems with external disturbances,” Transactions of the Institute of Measurement and Control, vol. 40, no. 13, pp. 3604–3616, September 2018.

    Article  Google Scholar 

  9. J.-J. Fu, Q. Wang, and J.-Z. Wang, “Robust finite-time consensus tracking for second-order multi-agent systems with input saturation under general directed communication graphs,” International Journal of Control, vol. 92, no. 8, pp. 1785–1795, August 2019.

    Article  MathSciNet  Google Scholar 

  10. S. Islam and N.I. Xiros, “Robust asymptotic and finite-time tracking for second-order nonlinear multi-agent autonomous systems,” International Journal of Control, Automation, and Systems, vol. 17, no. 12, pp. 3069–3078, December 2019.

    Article  Google Scholar 

  11. A. Polyakov, “Nonlinear feedback design for fixed-time stabilization of linear control systems,” IEEE Transactions on Automatic Control, vol. 57, no. 8, pp. 2106–2110, August 2012.

    Article  MathSciNet  Google Scholar 

  12. A. Khanzadeh and M. Pourgholi, “Fixed-time leader-follower consensus tracking of second-order multi-agent systems with bounded input uncertainties using nonsingular terminal sliding mode technique,” IET Control Theory and Applications, vol. 12, no. 5, pp. 679–686, 2018.

    Article  MathSciNet  Google Scholar 

  13. J.-K. Ni, L. Liu, C.-X. Liu, and J. Liu, “Fixed-time leader-following consensus for second-order multiagent systems with input delay,” IEEE Transactions on Industrial Electronics, vol. 64, no. 11, pp. 8635–8646, November 2017.

    Article  Google Scholar 

  14. J.-K. Ni, Y. Tang, and P. Shi, “A new fixed-time consensus tracking approach for second-Order multiagent systems under directed communication topology,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, May 2019.

  15. J. Cheng, Y.-N. Shan, J.-D. Cao, and J.-H. Park, “Non-stationary control for TS fuzzy Markovian switching systems with variable quantization density,” IEEE Transactions on Fuzzy Systems, 2020. DOI: https://doi.org/10.1109/TFUZZ.2020.2974440

  16. J. Cheng, D. Zhang, W.-H. Qi, J.-D. Cao, and K.-B. Shi, “Finite-time stabilization of T-S fuzzy semi-Markov switching systems: A coupling memory sampled-data control approach,” Journal of the Franklin Institute, vol. 357, no. 16, pp. 11265–11280, November 2020.

    Article  MathSciNet  Google Scholar 

  17. M. Defoort, A. Polyakov, G. Demesure, M. Djemai, and K. Veluvolu, “Leader-follower fixed-time consensus for multi-agent systems with unknown non-linear inherent dynamics,” IET Control Theory and Applications, vol. 9, no. 14, pp. 2165–2170, September 2015.

    Article  MathSciNet  Google Scholar 

  18. H. Wang, W.-W. Yu, G.-H. Wen, and G.-R. Chen, “Fixed-time consensus of nonlinear multi-agent systems with general directed topologies,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 66, no. 9, pp. 1587–1591, September 2019.

    Article  Google Scholar 

  19. H. Li, M. Zhu, Z.-B. Chu, H.-B. Du, G.-H. Wen, and N. D. Alotaibi, “Fixed-time synchronization of a class of second-order nonlinear leader-following multi-agent systems,” Asian Journal of Control, vol. 20, no. 1, pp. 39–48, January 2018.

    Article  MathSciNet  Google Scholar 

  20. H.-B. Du, G.-H. Wen, D. Wu, Y.-Y. Cheng, and J.-H. Lu, “Distributed fixed-time consensus for nonlinear heterogeneous multi-agent systems,” Automatica, vol. 113, pp. 108797, March 2020.

    Article  MathSciNet  Google Scholar 

  21. Y. Huang and Y.-M. Jia, “Fixed-time consensus tracking control of second-order multi-agent systems with inherent nonlinear dynamics via output feedback,” Nonlinear Dynamics, vol. 91, no. 2, pp. 1289–1306, January 2018.

    Article  Google Scholar 

  22. P. Zhang, Y.-Z. Cong, D. Wu, G.-R. Zhang, and Q. Tan, “Design of fixed-time synchronization algorithm with applications,” International Journal of Advanced Robotic Systems, vol. 16, no. 6, pp. 462–472, November 2019.

    Google Scholar 

  23. H.-F. Hong, W.-W. Yu, J.-J. Fu, and X.-H. Yu, “A novel class of distributed fixed-time consensus protocols for second-order nonlinear and disturbed multi-agent systems,” IEEE Transactions on Network Science and Engineering, vol. 6, no. 4, pp. 760–772, October 2019.

    Article  MathSciNet  Google Scholar 

  24. G.-H. Wen, G.-Q. Hu, W.-W. Yu, J.-D. Cao, and G.-R. Chen, “Consensus tracking for higher-order multi-agent systems with switching directed topologies and occasionally missing control inputs,” Systems & Control Letters, vol. 62, no. 12, pp. 1151–1158, October 2019.

    Article  MathSciNet  Google Scholar 

  25. V. Andrieu, L. Praly, and A. Astolfi, “Homogeneous approximation, recursive observer design, and output feedback,” SIAM Journal on Control and Optimization, vol. 47, no. 4, pp. 1814–1850, 2008.

    Article  MathSciNet  Google Scholar 

  26. M. Goldberg, “Equivalence constants for 1p norms of matrices,” Linear Multilinear & Algebra, vol. 21, no. 2, pp. 173–179, 1987.

    Article  MathSciNet  Google Scholar 

  27. D. S. Mitrinovic and P. M. Vasic, Analytic Inequalities, Springer-verlag Press, Berlin, 1970.

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute of Automation, Jiangnan University, Wuxi, 214122, China

    Cong Wang & Cheng-Lin Liu

  2. School of Automation, Southeast University, Nanjing, 210096, China

    Yang-Yang Chen & Ya Zhang

Authors
  1. Cong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cheng-Lin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yang-Yang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ya Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cheng-Lin Liu.

Additional information

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

This work was supported by the National Natural Science Foundation of China under Grants 61973139 and 61473138, the Fundamental Research Funds for the Central Universities under Grant JUSRP22014 and the Six Talent Peaks Project in Jiangsu Province under Grant 2015-DZXX-011.

Cong Wang received his B.Sc. degree in automation from Jiangnan University, China, in 2014, where he is currently pursuing an M.Sc. degree. His research interests include sliding mode control, fixed-time control, and multi-agent systems.

Cheng-Lin Liu received his Bachelor degree in electrical engineering and automation from Nanjing University of Science and Technology, China in 2003 and a Ph.D. degree in Control Theory and Control Engineering from Southeast University, China in 2008. Since 2008, he has been with Jiangnan University, Wuxi, China, where he is currently a professor at Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of IOT Engineering. From March 2014 to March 2015, he was with the School of Electrical and Electronic Engineering at Nanyang Technological University as a visiting scholar. His current research interests include coordination control of multi-agent systems, iterative learning control, and nonlinear control.

Yang-Yang Chen received his B.Sc. and M.Sc. degrees in electrical engineering and automation from the Hefei University of Technology, Hefei, China, in 2003 and 2006, respectively, and a Ph.D. degree in control science and engineering from Southeast University, Nanjing, China, in 2010. Since 2010, he has been with Southeast University, where he is currently an Associated Professor with the School of Automation. His current research interests include adaptive control, nonlinear formation control, and coordinated path-following control.

Ya Zhang received her B.S. degree in applied mathematics from China University of Mining and Technology in 2004, and a Ph.D. degree in control engineering from Southeast University, China, in 2010. Since 2010, she has been with Southeast University, Nanjing, China, where she is currently a professor with the School of Automation. Her research interests include cooperative control and estimation, multi-agent systems, and network security.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, C., Liu, CL., Chen, YY. et al. Fixed-time Consensus Tracking for Second-order Leader-follower Multi-agent Systems with Nonlinear Dynamics Under Directed Topology. Int. J. Control Autom. Syst. 19, 2697–2705 (2021). https://doi.org/10.1007/s12555-020-0321-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-020-0321-0

Keywords

Search

Navigation