[go: up one dir, main page]
Skip to main content

Advertisement

Springer Nature Link
Log in

Observer-based impulsive control for finite-time synchronization of delayed neural networks on time scales

  • Original Research
  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

This paper investigates the finite-time synchronization (FTS) of delayed neural networks on time scales via impulsive control. First, an impulsive controller is designed when system states are accessible. Based on the time scale theory and mathematical induction method, a sufficient condition for FTS is presented. Then, an observer is provided to estimate system states when partial states can not be available. An observer-based impulsive controller is devised to ensure that both the observer error system and the synchronization error system converges to zero in finite time. Furthermore, the explicit expression for settling time of the FTS is given. Finally, the validity of our methods is verified by a numerical simulation.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Data availibility

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

References

  1. Gao, X., Mou, J., Banerjee, S., Zhang, Y.: Color-gray multi-image hybrid compression-encryption scheme based on bp neural network and knight tour. IEEE Trans. Cybern. 53(8), 5037–5047 (2023)

    Article  MATH  Google Scholar 

  2. Xiong, Z., Cai, Z., Hu, C., Takabi, D., Li, W.: Towards neural network-based communication system: Attack and defense. IEEE Trans. Dependable Secur. Comput. 20(4), 3238–3250 (2023)

    Article  MATH  Google Scholar 

  3. Zhou, Y., Jiao, X.: Intelligent analysis system for signal processing tasks based on lstm recurrent neural network algorithm. Neural Comput. Appl. 34(15), 12257–12269 (2022)

    Article  MATH  Google Scholar 

  4. Huang, Z., Wang, M., Silvestre, C., Gorbachev, S., Cao, J.: A time-scale integral delay inequality approach for antisynchronization of neural networks via impulsive controllers. IEEE Trans. Control Netw. Syst. 10(1), 194–204 (2023)

    Article  MathSciNet  MATH  Google Scholar 

  5. Gu, Y., Wang, H., Yu, Y.: Stability and synchronization of fractional-order generalized reaction-diffusion neural networks with multiple time delays and parameter mismatch. Neural Comput. Appl. 34(20), 17905–17920 (2022)

    Article  MATH  Google Scholar 

  6. Chen, J., Zhang, X., Park, J.H., Xu, S.: Improved stability criteria for delayed neural networks using a quadratic function negative-definiteness approach. IEEE Trans. Neural Netw. Learn. Syst. 33(3), 1348–1354 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  7. Li, R., Gao, X., Cao, J.: Exponential synchronization of stochastic memristive neural networks with time-varying delays. Neural Process. Lett. 50(1), 459–475 (2019)

    Article  MATH  Google Scholar 

  8. Oliveira, J.J.: Global exponential stability of discrete-time hopfield neural network models with unbounded delays. J. Differ. Equ. Appl. 28(5), 725–751 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  9. Li, Z., Fang, J.-A., Huang, T., Miao, Q., Wang, H.: Impulsive synchronization of discrete-time networked oscillators with partial input saturation. Inf. Sci. 422, 531–541 (2018)

    Article  MATH  Google Scholar 

  10. Bohner, M., Peterson, A.: Dynamic Equations on Time Scales: An Introduction with Applications. Springer, Berlin (2001)

    Book  MATH  Google Scholar 

  11. Bohner, M., Peterson, A.C.: Advances in Dynamic Equations on Time Scales. Springer, Berlin (2002)

    MATH  Google Scholar 

  12. Dai, L., Li, Z.: Almost periodic synchronization for complex-valued neural networks with time-varying delays and impulsive effects on time scales. J. Appl. Anal. Comput. 13(2), 893–912 (2023)

    MathSciNet  MATH  Google Scholar 

  13. Wan, P., Zeng, Z.: Global exponential stability of impulsive delayed neural networks on time scales based on convex combination method. IEEE Trans. Syst. Man Cybern. Syst. 52(5), 3015–3024 (2022)

    Article  MATH  Google Scholar 

  14. Zhang, X., Lu, X., Liu, Z.: Razumikhin and krasovskii methods for asymptotic stability of nonlinear delay impulsive systems on time scales. Nonlinear Anal. Hybrid Syst. 32, 1–9 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  15. Amato, F., Ariola, M., Dorato, P.: Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica 37(9), 1459–1463 (2001)

    Article  MATH  Google Scholar 

  16. Huang, Y., Wu, F.: Finite-time passivity and synchronization of coupled complex-valued memristive neural networks. Inf. Sci. 580, 775–800 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  17. Luo, Z., Wang, J.: Finite time stability analysis of systems based on delayed exponential matrix. J. Appl. Math. Comput. 55, 335–351 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  18. Ji, M., He, Y., Wu, M., Zhang, C.: Further results on exponential stability of neural networks with time-varying delay. Appl. Math. Comput. 256, 175–182 (2015)

    MathSciNet  MATH  Google Scholar 

  19. Gunasekaran, N., Ali, M.S., Pavithra, S.: Finite-time L-infinity performance state estimation of recurrent neural networks with sampled-data signals. Neural Process. Lett. 51(2), 1379–1392 (2020)

    Article  MATH  Google Scholar 

  20. Liu, X., Su, H., Chen, M.Z.: A switching approach to designing finite-time synchronization controllers of coupled neural networks. IEEE Trans. Neural Netw. Learn. Syst. 27(2), 471–482 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  21. Rong, N., Wang, Z., Xie, X., Ding, S.: Event-triggered synchronization for discrete-time neural networks with unknown delays. IEEE Trans. Circuits Syst. II Expr. Briefs 68(10), 3296–3300 (2021)

    MATH  Google Scholar 

  22. Wang, B., Zhang, Y., Zhang, B.: Exponential synchronization of nonlinear complex networks via intermittent pinning control on time scales. Nonlinear Anal. Hybrid Syst. 37(100903), 1–18 (2020)

    MathSciNet  MATH  Google Scholar 

  23. Yang, X., Lu, J.: Finite-time synchronization of coupled networks with markovian topology and impulsive effects. IEEE Trans. Autom. Control 61(8), 2256–2261 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  24. Wang, S., Cao, Y., Huang, T., Chen, Y., Wen, S.: Event-triggered distributed control for synchronization of multiple memristive neural networks under cyber-physical attacks. Inf. Sci. 518, 361–375 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  25. Aravind, R.V., Balasubramaniam, P.: Global asymptotic stability of delayed fractional-order complex-valued fuzzy cellular neural networks with impulsive disturbances. J. Appl. Math. Comput. 68(6), 4713–4731 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  26. Pan, L., Song, Q., Cao, J., Ragulskis, M.: Pinning impulsive synchronization of stochastic delayed neural networks via uniformly stable function. IEEE Trans. Neural Netw. Learn. Syst. 33(9), 4491–4501 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  27. Wang, N., Li, X., Lu, J.: Impulsive-interaction-driven synchronization in an array of coupled neural networks. Neural Process. Lett. 51(3), 2685–2700 (2020)

    Article  MATH  Google Scholar 

  28. Tang, Z., Xuan, D., Park, J.H., Wang, Y., Feng, J.: Impulsive effects based distributed synchronization of heterogeneous coupled neural networks. IEEE Trans. Netw. Sci. Eng. 8(1), 498–510 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  29. Ji, X., Lu, J., Jiang, B., Shi, K.: Distributed synchronization of delayed neural networks: Delay-dependent hybrid impulsive control. IEEE Trans. Netw. Sci. Eng. 9(2), 634–647 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  30. Liu, X., Zhang, K.: Synchronization of linear dynamical networks on time scales: Pinning control via delayed impulses. Automatica 72, 147–152 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  31. Li, L., Jiang, W., Tu, Z.: Saturated impulsive control for delayed nonlinear complex dynamical networks on time scales. Appl. Math. Model 119, 54–67 (2023)

    Article  MathSciNet  MATH  Google Scholar 

  32. Huang, Z., Cao, J., Li, J., Bin, H.: Quasi-synchronization of neural networks with parameter mismatches and delayed impulsive controller on time scales. Nonlinear Anal. Hybrid Syst. 33, 104–115 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  33. Lu, X., Zhang, X., Liu, Q.: Finite-time synchronization of nonlinear complex dynamical networks on time scales via pinning impulsive control. Neurocomputing 275, 2104–2110 (2018)

    Article  MATH  Google Scholar 

  34. Zheng, G., Orlov, Y., Perruquetti, W., Richard, J.P.: Finite-time-observer design for nonlinear impulsive systems with impact perturbation. Int. J. Control 87(10), 2097–2105 (2014)

    MathSciNet  MATH  Google Scholar 

  35. Wang, Y., Li, X., Song, S.: Exponential synchronization of delayed neural networks involving unmeasurable neuron states via impulsive observer and impulsive control. Neurocomputing 441, 13–24 (2021)

    Article  MATH  Google Scholar 

  36. Wang, Y., Li, X.: Impulsive observer and impulsive control for time-delay systems. J. Franklin Inst. 357(13), 8529–8542 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  37. Wu, Y., Li, Y., Li, W.: Almost surely exponential synchronization of complex dynamical networks under aperiodically intermittent discrete observations noise. IEEE Trans. Cybern. 52(5), 1–12 (2020)

    MATH  Google Scholar 

  38. Dey, S., Taousser, F.Z., Djemai, M., Defoort, M., Di Gennaro, S.: Observer based leader-follower bipartite consensus with intermittent failures using lyapunov functions and time scale theory. IEEE Control Syst. Lett. 5(6), 1904–1909 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  39. Dorato, P.: Short-Time Stability in Linear Time-varying Systems, pp. 83–87. Polytechnic Institute of Brooklyn, Brooklyn (1961)

    MATH  Google Scholar 

Download references

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 62003189, 61973189], the China Postdoctoral Science Foundation [grant numbers 2020M672024], the Natural Science Foundation of Shandong Province[grant numbers ZR2021MA016, ZR2021MA043].

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, China

    Chuan Zhang, Ruihong Liu & Yingxin Guo

  2. School of Control Science and Engineering, Shandong University, Jinan, 250061, Shandong, China

    Xianfu Zhang

Authors
  1. Chuan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ruihong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xianfu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yingxin Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chuan Zhang.

Ethics declarations

Conflict of interest

We declare no Conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, C., Liu, R., Zhang, X. et al. Observer-based impulsive control for finite-time synchronization of delayed neural networks on time scales. J. Appl. Math. Comput. 71, 627–642 (2025). https://doi.org/10.1007/s12190-024-02268-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-024-02268-0

Keywords