Skip to main content
SpringerLink
Log in

Error-constrained Coordinated Tracking Control for High-order Multiagent Systems Based on Barrier Lyapunov Function

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

Abstract

In this paper, the coordinated tracking problem of high-order multiagent systems with preset error constraints is studied. Based on the barrier Lyapunov function method, two novel distributed error-constrained consensus controllers are proposed: time-invariant symmetric error-constrained controller and time-varying asymmetric error-constrained controller. The first controller can meet the requirement of a fixed preset error bound for the system, and the system errors converge with the exponential rate. Then, the second controller is designed based on an error-constrained function and error transformation, which can not only meet the time-varying error constraint but also guarantee the lower bound of the convergence rate of the consensus error. That is, the transient performance of the system is guaranteed. Then, the effectiveness of the two controllers is verified and compared by a simulation example. Furthermore, a full-order error-constrained controller is designed by combining the above two methods, and its effectiveness is verified by the coordinated depth tracking simulation of multiple underwater vehicles.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520–1533, September 2004.

    Article  MathSciNet  Google Scholar 

  2. Y. C. Cao, W. Ren, and Y. Li, “Distributed discrete-time coordinated tracking with a time-varying reference state and limited communication,” Automatica, vol. 45, no. 5, pp. 1299–1305, May 2009.

    Article  MathSciNet  Google Scholar 

  3. F. Chen and J. Chen, “Minimum-energy distributed consensus control of multiagent systems: A network approximation approach,” IEEE Transactions on Automatic Control, vol. 65, no. 3, pp. 1144–1159, March 2020.

    Article  MathSciNet  Google Scholar 

  4. A. K. Pamosoaji, M. Piao, and K. S. Hong, “PSO-based minimum-time motion planning for multiple vehicles under acceleration and velocity limitations,” International Journal of Control, Automation, and Systems, vol. 17, no. 10, pp. 2610–2623, April 2019.

    Article  Google Scholar 

  5. H. S. Ahn and M. H. Trinh, “Consensus under biased alignment,” Automatica, vol. 110, December 2019.

  6. J. Liu, Y. Zhang, Y. Yu, and C. Sun, “A Zeno-free self-triggered approach to practical fixed-time consensus tracking with input delay,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, pp. 1–11, February 2021. DOI: https://doi.org/10.1109/TSMC.2021.3063117.

  7. C. C. Hua, Z. J. Li, K. Li, S. Z. Chen, and J. Sun, “Distributed control for uncertain nonlinear multiagent systems subject to hybrid faults,” International Journal of Control, Automation, and Systems, vol. 18, no. 10, pp. 2589–2598, May 2020.

    Article  Google Scholar 

  8. J. Liu, Y. Yu, H. He, and C. Sun, “Team-triggered practical fixed-time consensus of double-integrator agents with uncertain disturbance,” IEEE Transactions on Cybernetics, vol. 51, no. 6, pp. 3263–3273, 2021.

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. S. Bhowmick and S. Panja, “Leader-follower bipartite consensus of linear multiagent systems over a signed directed graph,” IEEE Transactions on Circuits and Systems II-Express Briefs, vol. 66, no. 8, pp. 1436–1440, August 2019.

    Article  Google Scholar 

  11. Y. Yang, D. Yue and C. Xu, “Dynamic event-triggered leader-following consensus control of a class of linear multi-agent systems,” Journal of the Franklin Institute-Engineering and Applied Mathematics, vol. 355, no. 15, pp. 7706–7734, October 2018.

    Article  MathSciNet  Google Scholar 

  12. Y. L. Wang, J. D. Cao, H. J. Wang, and F. E. Alsaadi, “Event-triggering consensus for second-order leader-following multiagent systems with nonlinear time-delayed dynamics,” International Journal of Control, Automation, and Systems, vol. 18, no. 5, pp. 1083–1093, May 2020.

    Article  Google Scholar 

  13. A. H. Hu, J. H. Park, and J. D. Cao, “Group consensus of multi-agent networks with hybrid interactions,” Neurocomputing, vol. 404, pp. 267–275, September 2020.

    Article  Google Scholar 

  14. M. A. Razaq, M. Rehan, M. Tufail, and C. K. Ahn, “Multiple Lyapunov functions approach for consensus of onesided Lipschitz multi-agents over switching topologies and input saturation,” IEEE Transactions on Circuits and Systems II-Express Briefs, vol. 67, no. 12, pp. 3267–3271, December 2020.

    Article  Google Scholar 

  15. J. Liu, Y. L. Zhang, Y. Yu, and C.Y. Sun, “Fixed-time leader-follower consensus of networked nonlinear systems via event/self-triggered control,” IEEE Transactions on Neural Networks and Learning Systems, vol. 31, no. 11, pp. 5029–5037, November 2020.

    Article  MathSciNet  Google Scholar 

  16. M. J. Park, O. M. Kwon, J. H. Park, S. M. Lee, J. W. Son, and E. J. Cha, “H-infinity consensus performance for discrete-time multi-agent systems with communication delay and multiple disturbances,” Neurocomputing, vol. 138, pp. 199–208, August 2014.

    Article  Google Scholar 

  17. H. S. Su, Y. Y. Ye, Y. Qiu, Y. Cao, and M. Z. Q. Chen, “Semi-global output consensus for discrete-time switching networked systems subject to input saturation and external disturbances,” IEEE Transactions on Cybernetics, vol. 49, no. 11, pp. 3934–3945, November 2019.

    Article  Google Scholar 

  18. F. Y. Wang, Y. H. Ni, Z. X. Liu, and Z. Q. Chen, “Containment control for general second-order multiagent systems with switched dynamics,” IEEE Transactions on Cybernetics, vol. 50, no. 2, pp. 550–560, February 2020.

    Article  Google Scholar 

  19. Z. G. Wu, Y. Xu, R. Q. Lu, Y. Q. Wu, and T. W. Huang, “Event-triggered control for consensus of multiagent systems with fixed/switching topologies,” IEEE Transactions on Systems Man Cybernetics: Systems, vol. 48, no. 10, pp. 1736–1746, October 2018.

    Article  Google Scholar 

  20. Z. Y. Zuo, B. L. Tian, M. Defoort, and Z. T. Ding, “Fixed-time consensus tracking for multiagent systems with highorder integrator dynamics,” IEEE Transactions on Automatic Control, vol. 63, no. 2, pp. 563–570, October 2018.

    Article  MathSciNet  Google Scholar 

  21. G. P. Li, X. Y. Wang, and S. H. Li, “Consensus control of higher-order Lipschitz non-linear multi-agent systems based on backstepping method,” IET Control Theory and Applications, vol. 14, no. 3, pp. 490–498, February 2020.

    Article  Google Scholar 

  22. N. Rahimi, T. Binazadeh, and M. Shasadeghi, “Observer-based consensus of higher-order nonlinear heterogeneous multiagent systems with unmatched uncertainties: Application on robotic systems,” Robotica, vol. 38, no. 9, pp. 1605–1626, September 2020.

    Article  Google Scholar 

  23. Z. Gallehdari, N. Meskin, and K. Khorasani, “A distributed control reconfiguration and accommodation for consensus achievement of multiagent systems subject to actuator faults,” IEEE Transactions on Control Systems Technology, vol. 24, no. 6, pp. 2031–2047, November 2016.

    Article  Google Scholar 

  24. J. Ghommam, S. El Ferik, and M. Saad, “Robust adaptive path-following control of underactuated marine vessel with off-track error constraint,” International Journal of Systems Science, vol. 49, no. 7, pp. 1540–1558, April 2018.

    Article  MathSciNet  Google Scholar 

  25. Y. H. Zhang, H. Y. Li, J. Sun, and W. He, “Cooperative adaptive event-triggered control for multiagent systems with actuator failures,” IEEE Transactions on Systems Man Cybernetics: Systems, vol. 49, no. 9, pp. 1759–1768, September 2019.

    Article  Google Scholar 

  26. M. Shahvali, A. Azarbahram, M. B. Naghibi-Sistani, and J. Askari, “Bipartite consensus control for fractional-order nonlinear multi-agent systems: An output constraint approach,” Neurocomputing, vol. 397, pp. 212–223, July 2020.

    Article  Google Scholar 

  27. K. P. Tee, B. Ren, and S. S. Ge, “Barrier Lyapunov functions for the control of output-constrained nonlinear systems,” Automatica, vol. 45, no. 4, pp. 918–927, January 2009.

    Article  MathSciNet  Google Scholar 

  28. B. Ren, S. S. Ge, K. P. Tee, and T. H. Lee, “Adaptive neural control for output feedback nonlinear systems using a barrier Lyapunov function,” IEEE Transactions on Neural Networks, vol. 21, no. 8, pp. 1339–1345, July 2010.

    Article  Google Scholar 

  29. Y. Jiang, C. Guo, and H. Yu, “Robust trajectory tracking control for an underactuated autonomous underwater vehicle based on bioinspired neurodynamics,” International Journal of Advanced Robotic Systems, vol. 15, no. 5, pp. 1–12, September 2018.

    Article  Google Scholar 

Download references

Funding

This work was supported by the Tianjin Natural Science Foundation of China under Grant (No. 20JCYBJC01060, 20JCQNJC01450), the National Natural Science Foundation of China under Grant 61973175, the Fundamental Research Funds for the Central Universities under Grant 63201196, and the Tianjin Research Innovation Project for Postgraduate Students under Grant 2020YJSZXB12.

Author information

Authors and Affiliations

  1. School of Artificial Intelligence, Nankai University, 38 Tongyan Road, Tianjin, 300350, China

    Yunbiao Jiang, Zhongxin Liu, Zengqiang Chen & Feng Duan

Authors
  1. Yunbiao Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhongxin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zengqiang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Feng Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Zhongxin Liu or Feng Duan.

Additional information

Yunbiao Jiang received his B.S. degree from Dalian Polytechnic University and an M.S. degree from Dalian Maritime University, Dalian, China, in 2016 and 2019, respectively. He is currently pursuing a Ph.D. degree with the College of Artificial Intelligence at Nankai University, Tianjin, China. His research interests include multi-agent systems, unmanned underwater vehicles, robust control, and fault-tolerant control.

Zhongxin Liu received his B.S. degree in automation and a Ph.D. degree in control theory and control engineering from Nankai University, Tianjin, China, in 1997 and 2002, respectively. He has been with Nankai University, where he is currently a Professor with the Department of Automation. His research interests include multiagent systems, nonlinear control theory, as well as complex network theory and its application.

Zengqiang Chen received his B.S. degree in mathematics and his M.S. and Ph.D. degrees in control theory and control engineering from Nankai University, Tianjin, China, in 1987, 1990, and 1997, respectively. He has been with Nankai University, where he is currently a Professor with the Department of Automation. His research interests include predictive control technology, complex network system, chaotic system theory and its application in information security.

Feng Duan received his B.E. and M.E. degrees in mechanical engineering from Tianjin University, Tianjin, China, in 2002 and 2004, respectively, and his M.S. and Ph.D. degrees in precision engineering from The University of Tokyo, Tokyo, Japan, in 2006 and 2009, respectively. He is currently a Professor with Nankai University, China. His research interests include cellular manufacture systems, rehabilitation robots, and brain machine interfaces.

Publisher’s Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jiang, Y., Liu, Z., Chen, Z. et al. Error-constrained Coordinated Tracking Control for High-order Multiagent Systems Based on Barrier Lyapunov Function. Int. J. Control Autom. Syst. 20, 1238–1249 (2022). https://doi.org/10.1007/s12555-021-0144-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-021-0144-7

Keywords

Search

Navigation