Skip to main content
SpringerLink
Log in

A Unified Framework for Finite-Time and Fixed-Time Stabilization of Neural Networks with General Activations and External Disturbances

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

This paper develops a unified framework to study the finite-time and fixed-time stabilization (FFTS) of neural networks (NNs) with general activations and external disturbances. A new distributed control algorithm is designed to achieve the goal of FFTS for the NNs with either continuous or discontinuous activations. An upper-bound of the stabilization time is determined based on the control parameters. Numerical simulations are provided to demonstrate the robustness and disturbance rejection of the proposed control algorithm.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. J.P. Aubin, A. Cellina, Differential Inclusions (Springer, Berlin, 1984)

    Book  MATH  Google Scholar 

  2. J.P. Aubin, H. Frankowska, Set-Valued Analysis (Birkhauser, Boston, 1990)

    MATH  Google Scholar 

  3. S. Bhat, D. Bernstein, Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38(3), 751–766 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. F.H. Clarke, Optimization and Nonsmooth Analysis (Wiley, New York, 1983)

    MATH  Google Scholar 

  5. A.F. Filippov, Differential Equations with Discontinuous Right-Hand Side, Mathematics and its Applications (Soviet Series) (Kluwer Academic Publishers, Boston, 1988)

    Book  Google Scholar 

  6. M. Forti, P. Nistri, Global convergence of neural networks with discontinuous neuron activations. IEEE Trans. Circuits Syst. I 50(11), 1421–1435 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Forti, P. Nistri, D. Papini, Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain. IEEE Trans. Neural Netw. 16(6), 1449–1463 (2005)

    Article  Google Scholar 

  8. G.H. Hardy, J.E. Littlewood, G. Pólya, Inequalities (Cambridge University Press, Cambridge, 1988)

    MATH  Google Scholar 

  9. H. Hong, W. Yu, G. Wen, X. Yu, Distributed robust fixed-time consensus for nonlinear and disturbed multiagent systems. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1464–1473 (2017)

    Article  Google Scholar 

  10. C. Hu, J. Yu, Z. Chen, H. Jiang, T. Huang, Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks. Neural Netw. 89, 74–83 (2017)

    Article  Google Scholar 

  11. X. Li, X. Fu, P. Balasubramaniam, R. Rakkiyappan, Existence, uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations. Nonlinear Anal. Real World Appl. 11(5), 4092–4108 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Q. Li, B. Shen, Y. Liu, T. Huang, Event-triggered H-infinity state estimation for discrete-time neural networks with mixed time delays and sensor saturations. Neural Comput. Appl. 28(12), 3815–3825 (2017)

    Article  Google Scholar 

  13. X. Liu, J. Cao, On periodic solutions of neural networks via differential inclusions. Neural Netw. 22(4), 329–334 (2009)

    Article  MATH  Google Scholar 

  14. X. Liu, J. Cao, W. Yu, Q. Song, Nonsmooth finite-time synchronization of switched coupled neural networks. Trans. Cybern. 46(10), 2360–2371 (2016)

    Article  Google Scholar 

  15. X. Liu, J. Cao, Robust state estimation for neural networks with discontinuous activations. IEEE Trans. Syst. Man Cybern. B Cybern. 40(6), 1425–1437 (2010)

    Article  Google Scholar 

  16. X. Liu, T. Chen, Finite-time and fixed-time cluster synchronization with or without pinning control. IEEE Trans. Cybern. 48(1), 240–252 (2018)

    Article  Google Scholar 

  17. X. Liu, T. Chen, J. Cao, W. Lu, Dissipativity and quasi-synchronization for neural networks with discontinuous activations and parameter mismatches. Neural Netw. 24(10), 1013–1021 (2011)

    Article  MATH  Google Scholar 

  18. X. Liu, D.W.C. Ho, Q. Song, W. Xu, Finite/fixed-time pinning synchronization of complex networks with stochastic disturbances. IEEE Trans. Cybern. (2018). https://doi.org/10.1109/TCYB.2018.2821119

    Google Scholar 

  19. X. Liu, J. Lam, W. Yu, G. Chen, Finite-time consensus of multiagent systems with a switching protocol. IEEE Trans. Neural Netw. Learn. Syst. 27(4), 853–862 (2016)

    Article  MathSciNet  Google Scholar 

  20. X. Liu, J.H. Park, N. Jiang, J. Cao, Nonsmooth finite-time stabilization of neural networks with discontinuous activations. Neural Netw. 52, 25–32 (2014)

    Article  MATH  Google Scholar 

  21. X. Liu, W. Yu, J. Cao, F. Alsaadi, Finite-time synchronisation control of complex networks via non-smooth analysis. IET Control Theory Appl. 9(8), 1245–1253 (2015)

    Article  MathSciNet  Google Scholar 

  22. W. Lu, T. Chen, Dynamical behaviors of delayed neural networks systems with discontinuous activation functions. Neural Comput. 18(3), 683–708 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  23. W. Lu, X. Liu, T. Chen, A note on finite-time and fixed-time stability. Neural Netw. 81, 11–15 (2016)

    Article  Google Scholar 

  24. J. Lu, D.W.C. Ho, J. Cao, J. Kurths, Exponential synchronization of linearly coupled neural networks with impulsive disturbances. IEEE Trans. Neural Netw. 22(2), 329–336 (2011)

    Article  Google Scholar 

  25. A. Polyakov, Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans. Autom. Control 57(8), 2106–2110 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  26. A. Polyakov, D. Efimov, W. Perruquetti, Finite-time and fixed-time stabilization: implicit Lyapunov function approach. Automatica 51, 332–340 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  27. J. Shen, J. Cao, Finite-time synchronization of coupled neural networks via discontinuous controllers. Cognit. Neurodynamics 5(4), 373–385 (2011)

    Article  Google Scholar 

  28. Y. Shen, J. Wang, Robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances. IEEE Trans. Neural Netw. Learn. Syst. 23(1), 87–96 (2012)

    Article  Google Scholar 

  29. B. Shen, Z. Wang, H. Qiao, Event-triggered state estimation for discrete-time multi delayed neural networks with stochastic parameters and incomplete measurements. IEEE Trans. Neural Netw. Learn. Syst. 28(5), 1152–1163 (2017)

    Article  Google Scholar 

  30. Y. Wan, J. Cao, G. Wen, W. Yu, Robust fixed-time synchronization of delayed Cohen–Grossberg neural networks. Neural Netw. 73, 86–94 (2016)

    Article  MATH  Google Scholar 

  31. L. Wang, Y. Shen, Z. Ding, Finite time stabilization of delayed neural networks. Neural Netw. 70, 74–80 (2015)

    Article  MATH  Google Scholar 

  32. L. Wang, Z. Zeng, J. Hu, X. Wang, Controller design for global fixed-time synchronization of delayed neural networks with discontinuous activations. Neural Netw. 87, 122–131 (2017)

    Article  Google Scholar 

  33. J. Wang, X. Zhang, Q. Han, Event-triggered generalized dissipativity filtering for neural networks with time-varying delays. IEEE Trans. Neural Netw. Learn. Syst. 27(1), 77–88 (2016)

    Article  MathSciNet  Google Scholar 

  34. R. Yang, H. Gao, J. Lam, P. Shi, New stability criteria for neural networks with distributed and probabilistic delays. Circuits Syst. Signal Process 28, 505–522 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  35. X. Yang, D.W.C. Ho, Synchronization of delayed memristive neural networks: robust analysis approach. IEEE Trans. Cybern. 46(12), 3377–3387 (2016)

    Article  Google Scholar 

  36. X. Yang, Q. Song, J. Liang, B. He, Finite-time synchronization of coupled discontinuous neural networks with mixed delays and nonidentical perturbations. J. Frankl. Inst. 352, 4382–4406 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  37. S. Yu, Z. Ma, Q. Zhu, D. Wu, Nonsmooth finite-time control of uncertain affine planar systems, in Proceedings of the 6th World Congress on Intelligent Control and Automation, pp. 21–23 (2006)

  38. X. Zhang, Q. Han, New Lyapunov–Krasovskii functionals for global asymptotic stability of delayed neural networks. IEEE Trans. Neural Netw. 20(3), 533–539 (2009)

    Article  Google Scholar 

  39. X. Zhang, Q. Han, Global asymptotic stability for a class of generalized neural networks with interval time-varying delays. IEEE Trans. Neural Netw. 22(8), 1180–1192 (2011)

    Article  Google Scholar 

  40. X. Zhang, Q. Han, Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach. Neural Netw. 54, 57–69 (2014)

    Article  MATH  Google Scholar 

  41. Z.Y. Zuo, L. Tie, Distributed robust finite-time nonlinear consensus protocols for multi-agent systems. Int. J. Syst. Sci. 47(6), 1366–1375 (2016)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants Nos. 61773185, 61573096, and in part by Qing Lan Project.

Author information

Authors and Affiliations

  1. Business School, Jiangsu Normal University, Xuzhou, 221116, China

    Nan Jiang

  2. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, China

    Xiaoyang Liu

  3. School of Mathematics, Southeast University, Nanjing, 210096, China

    Jinde Cao

  4. School of Electrical Engineering, Nantong University, Nantong, 226019, China

    Jinde Cao

Authors
  1. Nan Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaoyang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jinde Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaoyang Liu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jiang, N., Liu, X. & Cao, J. A Unified Framework for Finite-Time and Fixed-Time Stabilization of Neural Networks with General Activations and External Disturbances. Circuits Syst Signal Process 38, 1005–1022 (2019). https://doi.org/10.1007/s00034-018-0907-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-018-0907-4

Keywords

Search

Navigation