Skip to main content
SpringerLink
Log in

Fixed-time Group Consensus of Nonlinear Multi-agent Systems via Pinning Control

  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper deals with the fixed-time group consensus problem for multi-agent systems (MASs) subjected to exogenous disturbances. Firstly, two pinning control algorithms are constructed for MASs, which not only reduce the number of controllers but also achieve expected tracking consensus. Secondly, fixed-time group consensus is ensured by utilizing the algebraic graph theory, Lyapunov stability and fixed-time control technique. Finally, simulations are finally given for demonstrate the availability of the derived results.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. J. Pan, W. Li, and H. P. Zhang, “Control algorithms of magnetic suspension systems based on the improved double exponential reaching law of sliding mode control,” International Journal of Control Automation and Systems, vol. 16, no. 6, pp. 2878–2887, December 2018.

    Article  Google Scholar 

  2. J. Pan, X. Jiang, X. K. Wan, and W. Ding, “A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems,” International Journal of Control Automation and Systems, vol. 15, no. 3, pp. 1189–1197, June 2017.

    Article  Google Scholar 

  3. F. Ding, X. Zhang, and L. Xu, “The innovation algorithms for multivariable state-space models,” International Journal of Adaptive Control and Signal Processing, vol. 33, no. 11, pp. 1601–1608, Novemebr 2019.

    Article  MathSciNet  MATH  Google Scholar 

  4. X. Zhang and F. Ding, “Adaptive parameter estimation for a general dynamical system with unknown states,” International Journal of Robust and Nonlinear Control, vol. 30, no. 4, pp. 1351–1372, March 2020.

    Article  MathSciNet  Google Scholar 

  5. X. Zhang, F. Ding, and L. Xu, “Recursive parameter estimation methods and convergence analysis for a special class of nonlinear systems,” International Journal of Robust and Nonlinear Control, vol. 30, no. 4, pp. 1373–1393, March 2020.

    Article  MathSciNet  Google Scholar 

  6. T. D. Ma, Z. L. Zhang, and B. Cui, “Adaptive consensus of multi-agent systems via odd impulsive control,” Neurocomputing, vol. 321, no. 10, pp. 139–145, December 2018.

    Article  Google Scholar 

  7. J. Wu, Q. Deng, T. Han, and H. C. Yan, “Distributed bipartite tracking consensus of nonlinear multi-agent systems with quantized communication,” Neurocomputing, vol. 395, pp. 78–85, June 2020.

    Article  Google Scholar 

  8. F. Y. Wang, Z. X. Liu, and Z. Q. Chen, “Distributed containment control for second-order multi-agent systems with time delay and intermittent communication,” International Journal of Robust and Nonlinear Control, vol. 28, no. 18, pp. 5730–5746, September 2018.

    Article  MathSciNet  MATH  Google Scholar 

  9. P. Wang and Y. M. Jia, “Distributed containment control of second-order multi-agent systems with inherent nonlinear dynamics,” IET Control Theory and Applications, vol. 8, no. 4, pp. 277–287, 2014.

    Article  MathSciNet  Google Scholar 

  10. H. Xu, T. Li, X. Liu, W. Liu, and J. Dong, “Spreading dynamics of an online social rumor model with psychological factors on scale-free networks,” Physica A: Statistical Mechanics and its Applications, vol. 525, pp. 234–246, July 2019.

    Article  MathSciNet  Google Scholar 

  11. T. Han and W. X. Zheng, “Bipartite output consensus for heterogeneous multi-agent systems via output regulation approach,” IEEE Transactions on Circuits and Systems II: Express Briefs, 2020.

  12. H. Q. Pei, S. M. Chen, and Q. Lai, “A local flocking algorithm of multi-agent dynamic systems,” International Journal of Control, vol. 88, no. 11, pp. 2242–2249, May 2015.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  14. X. S. Zhan, J. Wu, T. Jiang, and W. Jiang, “Optimal performance of networked control systems under the packet dropouts and channel noise,” ISA Transactions, vol. 58, no. 5, pp. 214–221, September 2015.

    Article  Google Scholar 

  15. X. S. Zhan, L. L. Cheng, J. Wu, and X. H. Yan, “Modified tracking performance limitation of networked time-delay systems with two-channel constraints,” Journal of the Franklin Institute, vol. 356, no. 12, pp. 6401–6418, August 2019.

    Article  MathSciNet  MATH  Google Scholar 

  16. X. H. Chang, Q. Liu, Y. M. Wang, and J. Xiong, “Fuzzy peak-to-peak filtering for networked nonlinear systems with multipath data packet dropouts,” IEEE Transactions on Fuzzy Systems, vol. 27, no. 3, pp. 436–446, July 2018.

    Article  Google Scholar 

  17. J. W. Hu, X. S. Zhan, J. Wu, and H. C. Yan, “Optimal tracking performance of NCSs with time-delay and encoding-decoding constraints,” International Journal of Control Automation and Systems, vol. 18, no. 4, pp. 1012–1022, November 2020.

    Article  Google Scholar 

  18. Z. H. Guan, X. S. Zhan, and G. Feng, “Optimal tracking performance of MIMO discrete-time systems with communication constraints,” International Journal of Robust and Nonlinear Control, vol. 22, no. 13, pp. 1429–1439, May 2011.

    Article  MathSciNet  MATH  Google Scholar 

  19. X. S. Zhan, L. L. Cheng, J. Wu, and Q. S. Yang, “Optimal modified performance of MIMO networked control systems with multi-parameter constraints,” ISA Transactions, vol. 84, no. 1, pp. 111–117, 2019.

    Article  Google Scholar 

  20. H. Shen, Y. Wang, J. W. Xia, J. H. Park, and Z. Wang, “Fault-tolerant leader-following consensus for multi-agent systems subject to semi-Markov switching topologies: An event-triggered control scheme,” Nonlinear Analysis: Hybrid Systems, vol. 34, pp. 92–107, November 2019.

    MathSciNet  MATH  Google Scholar 

  21. J. P. Zhou, Y. Wang, X. Zheng, Z. Wang, and H. Shen, “Weighted H∞ consensus design for stochastic multi-agent systems subject to external disturbances and ADT switching topologies,” Nonlinear Dynamics, vol. 96, pp. 853–868, February 2019.

    Article  MATH  Google Scholar 

  22. D. Zhao, T. Dong, and W. Hu, “Event-triggered consensus of discrete time second-order multi-agent networks,” International Journal of Control Automation and Systems, vol. 16, no. 1, pp. 87–96, March 2018.

    Article  Google Scholar 

  23. X. H. Chang, J. Xiong, and J. H. Park, “Estimation for a class of parameter-controlled tunnel diode circuits,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018. DOI:https://doi.org/10.1109/TSMC.2018.2859933

  24. J. P. Zhou, C. Y. Sang, X. Li, M. Y. Fang, and Z. Wang, “H∞ consensus for nonlinear stochastic multi-agent systems with time delay,” Applied Mathematics and Computation, vol. 325, pp. 41–58, May 2018.

    Article  MathSciNet  MATH  Google Scholar 

  25. L. Ding and W. X. Zheng, “Network-based practical consensus of heterogeneous nonlinear multi-agent systems,” IEEE Transactions on Cybernetics, vol. 47, no. 8, pp. 1841–1851, September 2016.

    Article  Google Scholar 

  26. G. H. Wen, H. Wang, X. H. Yu, and W. Yu, “Bipartite tracking consensus of linear multi-agent systems with a dynamic leader,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 65, no. 9, pp. 1204–1208, November 2017.

    Article  Google Scholar 

  27. J. Wu, Q. Deng, C. Y. Chen, and H. Yan. “Bipartite consensus for second order multi-agent systems with exogenous disturbance via pinning control,” IEEE Access, vol. 7, pp. 186563–186571, December 2019.

    Article  Google Scholar 

  28. D. M. Xie, L. Shi, and F. C. Jiang, “Second-order group consensus for linear multi-agent systems with average dwell time switching,” Transactions of the Institute of Measurement and Control, vol. 41, no. 2, pp. 484–493, April 2018.

    Article  Google Scholar 

  29. Y. Han, W. Lu, and T. Chen, “Couple-group consensus conditions for general first-order multi-agent systems with communication delays,” Systems and Control Letters, vol. 117, pp. 37–44, July 2018.

    Article  MathSciNet  Google Scholar 

  30. Y. Z. Feng and W. X. Zheng, “Group consensus control for discrete-time heterogeneous first- and second-order multiagent systems,” IET Control Theory and Applications, vol. 12, no. 6, pp. 753–760, April 2018.

    Article  MathSciNet  Google Scholar 

  31. Q. Ma, Z. Wang, and G. Y. Miao, “Second-order group consensus for multi-agent systems via pinning leader-following approach,” Journal of the Franklin Institute, vol. 351, no. 3, pp. 1288–1300, March 2014.

    Article  MATH  Google Scholar 

  32. X. S. Zhan, Z. H. Guan, X. H. Zhang, and F. S. Yuan, “Optimal tracking performance and design of networked control systems with packet dropout,” Journal of the Franklin Institute, vol. 350, no. 10, pp. 3205–3216, December 2013.

    Article  MathSciNet  MATH  Google Scholar 

  33. T. F. Ding, M. F. Ge, Z. W. Liu, Y. W. Wang, and H. R. Karimi, “Discrete-communication-based bipartite tracking of networked robotic systems via hierarchical hybrid control,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 67, no. 4, pp. 1402–1412, April 2020.

    Article  MathSciNet  Google Scholar 

  34. D. Huang, H. J. Jiang, Z. Yu, C. Kang, and C. Hu, “Leader-following cluster consensus in multi-agent systems with intermittence,” International Journal of Control Automation and Systems, vol. 16, no. 2, pp. 437–451, March 2018.

    Article  Google Scholar 

  35. X. S. Zhan, W. H. Zhang, J. Wu, and H. Yan. “Performance analysis of NCSs under channel noise and bandwidth constraints,” IEEE Access, vol. 8, pp. 20279–20288, January 2020.

    Article  Google Scholar 

  36. F. Ding, “Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling,” Applied Mathematical Modelling, vol. 37, no. 4, pp. 1694–1704, April 2013.

    Article  MathSciNet  MATH  Google Scholar 

  37. F. Ding, “Combined state and least squares parameter estimation algorithms for dynamic systems,” Applied Mathematical Modelling, vol. 38, no. 1, pp. 403–412, January 2014.

    Article  MathSciNet  MATH  Google Scholar 

  38. F. Ding, “State filtering and parameter estimation for state space systems with scarce measurements,” Signal Processing, vol. 104, pp. 369–380, November 2014.

    Article  Google Scholar 

  39. Y. Kim and M. Mesbahi, “On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian,” IEEE Transactions on Automatic Control, vol. 51, no. 1, pp. 116–120, August 2006.

    Article  MathSciNet  MATH  Google Scholar 

  40. S. Parsegov, A. Polyakov, and P. Shcherbakov, “Fixed-time consensus algorithm for multi-agent systems with integrator dynamics,” Proc. of 4th IFAC Workshop on Distributed Estimation and Control in Networked Systems, vol. 46, no. 27, pp. 110–115, 2013.

    Google Scholar 

  41. Z. Y. Zuo, B. L. Tian, M. Defoort, and Z. T. Ding, “Fixed-time consensus tracking for multi-agent systems with highorder integrator dynamics,” IEEE Transactions on Automatic Control, vol. 63, no. 2, pp. 563–570, July 2017.

    Article  MATH  Google Scholar 

  42. M. F. Ge, Z. W. Liu, G. H. Wen, X. H. Yu, and T. W. Huang, “Hierarchical controller-estimator for coordination of networked Euler-Lagrange systems,” IEEE Transactions on Cybernetics, vol. 50, no. 6, pp. 2450–2461, 2020.

    Article  Google Scholar 

  43. H. G. Zhang, J. Duan, Y. C. Wang, and Z. Y. Gao, “Bipartite fixed-time output consensus of heterogeneous linear multiagent systems,” IEEE Transactions on Cybernetics, 2019. DOI: https://doi.org/10.1109/TCYB.2019.2936009

  44. Y. L. Shang and Y. M. Ye, “Fixed-time group tracking control with unknown inherent nonlinear dynamics,” IEEE Access, vol. 5, no. 1, pp. 12833–12842, July 2017.

    Article  Google Scholar 

  45. Q. Deng, J. Wu, T. Han, Q. S. Yang, and X. S. Cai, “Fixed-time bipartite consensus of multi-agent systems with disturbances,” Physica A: Statistical Mechanics and its Applications, vol. 516, pp. 37–49, February 2019.

    Article  MathSciNet  Google Scholar 

  46. Y. J. Zhou, G. P. Jiang, F. Y. Xu, and Q. Y. Chen, “Distributed finite time consensus of second-order multi-agent systems via pinning control,” IEEE Access, vol. 6, pp. 45617–45624, August 2018.

    Article  Google Scholar 

  47. M. Mesbahi and M. Egerstedt, Graph Theoretic Methods in Multi-agent Networks, Princeton University Press, vol. 33, 2010.

  48. A. Filippov, Differential Equations with Discontinuous Righthand Sides: Control Systems, Springer Science and Business Media, vol. 18, 2013.

  49. F. Ding, L. Lv, J. Pan, X. K. Wan, and X. B. Jin, “Two-stage gradient-based iterative estimation methods for controlled autoregressive systems using the measurement data,” International Journal of Control Automation and Systems, vol. 18, no. 4, pp. 886–896, April 2020.

    Article  Google Scholar 

  50. F. Ding, X. P. Liu, and G. Liu, “Gradient based and least-squares based iterative identification methods for OE and OEMA systems,” Digital Signal Processing, vol. 20, no. 3, pp. 664–677, May 2010.

    Article  Google Scholar 

  51. F. Ding, X. G. Liu, and J. Chu, “Gradient-based and leastsquares-based iterative algorithms for Hammerstein systems using the hierarchical identification principle,” IET Control Theory and Applications, vol. 7, no. 2, pp. 176–184, February 2013.

    Article  MathSciNet  Google Scholar 

  52. X. K. Wan, Y. Li, C. Xia, M. H. Wu, J. Liang, and N. Wang, “A T-wave alternans assessment method based on least squares curve fitting technique,” Measurement, vol. 86, pp. 93–100, May 2016.

    Article  Google Scholar 

  53. F. Ding, Y. J. Liu, and B. Bao, “Gradient based and least squares based iterative estimation algorithms for multiinput multi-output systems,” Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 226, no. 1, pp. 43–55, February 2012.

    Article  Google Scholar 

  54. X. Zhang, F. Ding, and E. F. Yang, “State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors,” International Journal of Adaptive Control and Signal Processing, vol. 33, no. 7, pp. 1157–1173, July 2019.

    Article  MathSciNet  MATH  Google Scholar 

  55. F. Ding, L. Xu, D. D. Meng, X. K. Wan, and X. B. Jin, “Gradient estimation algorithms for the parameter identification of bilinear systems using the auxiliary model,” Journal of Computational and Applied Mathematics, vol. 369, p. 112575, May 2020.

    Article  MathSciNet  MATH  Google Scholar 

  56. X. Hu, X. S. Zhan, J. Wu, and H. Yan, “Performance of SIMO networked time-delay systems with encoding-decoding and quantization constraints,” IEEE Access, vol. 8, pp. 55125–55134, March 2020.

    Article  Google Scholar 

  57. T. Han, Z. H. Guan, B. Xiao, J. Wu, and X. Chen, “Distributed output consensus of heterogeneous multi-agent systems via an output regulation approach,” Neurocomputing, vol. 360, pp. 131–137, September 2019.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of College of Mechatronics and Control Engineering, Hubei Normal University, Huangshi, 435002, China

    Lili Hao, Xisheng Zhan, Jie Wu & Tao Han

  2. School of Information Science and Engineering, East China University of Science and Technology, Shanghai, 200237, China

    Huaicheng Yan

Authors
  1. Lili Hao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xisheng Zhan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jie Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tao Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Huaicheng Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xisheng Zhan.

Additional information

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

Recommended by Associate Editor Xiao-Heng Chang under the direction of Editor Jessie (Ju H.) Park. This paper was partially supported by the National Natural Science Foundation of China under Grants 61971181 and 61602163, the Youth Technology Innovation Team of Hubei Province under Grant T201710, the Natural Science Foundation of Hubei Province under Grants 2017CFA034 and 2019CFB226.

Lili Hao is pursuing an M.S. degree in College of Mechatronics and Control Engineering, Hubei Normal University, Huangshi, China. She received her B.S. degree in mathematics and statistics, Shangqiu Normal University, Shangqiu, China in 2018. She research interest includes cooperative control of multi-agent systems and complex networks.

Xisheng Zhan is a professor in College of Mechatronics and Control Engineering, Hubei Normal University. He received his B.S. and M.S. degrees in control theory and control engineering from the Liaoning Shihua University, Fushun, China, in 2003 and in 2006, respectively. He received his Ph.D. degree in control theory and applications from the Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, China, in 2012. His research interests include networked control systems, robust control and iterative learning control.

Jie Wu is an associate professor in College of Mechatronics and Control Engineering, Hubei Normal University. She received her B.S. and M.S. degrees in control theory and control engineering from the Liaoning Shihua University, Fushun, China, in 2004 and in 2007, respectively. Her research interests include networked control systems, robust control and complex network.

Tao Han received his Ph.D. degree in the College of Automation, Huazhong University of Science and Technology, Wuhan, China in 2017, and he is currently a lecturer in the College of Mechatronics and Control Engineering, Hubei Normal University. His research interest includes cooperative control of multi-agent systems and complex networks.

Huaicheng Yan is a Professor with the School of Information Science and Engineering, East China University of Science and Technology. He received his B.S. degree in automatic control from Wuhan University of Technology, Wuhan, China, in 2001, and received a Ph.D. degree in control theory and control engineering from the Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, China, in 2007. His current research interests include net-worked systems and multi-agent systems, etc.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hao, L., Zhan, X., Wu, J. et al. Fixed-time Group Consensus of Nonlinear Multi-agent Systems via Pinning Control. Int. J. Control Autom. Syst. 19, 200–208 (2021). https://doi.org/10.1007/s12555-019-1005-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-019-1005-5

Keywords

Search

Navigation