Skip to main content
SpringerLink
Log in

Synchronization Control for Chaotic Neural Networks with Mixed Delays Under Input Saturations

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

This paper is concerned with the exponential synchronization problem for chaotic neural networks with discrete and distributed delays under input saturations. Attention is focused on the design of saturated feedback controller such that the synchronization error system is locally exponentially stable. Based on delay-dependent sector conditions and augmented Lyapunov–Krasovskii functionals, sufficient conditions are established in the framework of linear matrix inequalities. Moreover, the optimization problems are proposed to maximize the estimate of the domain of attraction. Finally, two simulation examples show the effectiveness and benefit of the obtained 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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Aouiti C, Li X, Miaadi F (2019) A new LMI approach to finite and fixed time stabilization of high-order class of BAM neural networks with time-varying delays. Neural Process Lett 50:815–838

    Google Scholar 

  2. Baldi P, Atiya AF (1994) How delays affect neural dynamics and learning. IEEE Trans Neural Netw 5(4):612–621

    Google Scholar 

  3. Cao J, Lu J (2006) Adaptive synchronization of neural networks with or without time-varying delay. Chaos 16(1):013133

    MathSciNet  MATH  Google Scholar 

  4. Chen G, Dong X (1998) From Chaos to order: methodologies, perspectives, and applications. World Scientific, Singapore

    MATH  Google Scholar 

  5. Chen G, Sun J, Xia J (2020) Estimation of domain of attraction for aperiodic sampled-data switched delayed neural networks subject to actuator saturation. IEEE Trans Neural Netw Learn Syst 31(5):1489–1503

    MathSciNet  Google Scholar 

  6. Chen Y, Fei S, Li Y (2017) Robust stabilization for uncertain saturated time-delay systems: a distributed-delay-dependent polytopic approach. IEEE Trans Autom Control 62(7):3455–3460

    MathSciNet  MATH  Google Scholar 

  7. Chen Y, Wang Z, Liu Y, Alsaadi FE (2018) Stochastic stability for distributed delay neural networks via augmented Lyapunov–Krasovskii functionals. Appl Math Comput 338:869–881

    MathSciNet  MATH  Google Scholar 

  8. Chen Y, Wang Z, Shen B, Dong H (2019) Exponential synchronization for delayed dynamical networks via intermittent control: dealing with actuator saturations. IEEE Trans Neural Netw Learn Syst 30(4):1000–1013

    MathSciNet  Google Scholar 

  9. Chen Y, Wang Z, Han QL, Hu J (2021) Synchronization control for discrete-time delayed dynamical networks with switching topology under actuator saturations. IEEE Trans Neural Netw Learn Syst 32(5):2040–2053

    MathSciNet  Google Scholar 

  10. Fridman E, Pila A, Shaked U (2003) Regional stabilization and \(H_\infty \) control of time-delay systems with saturating actuators. Int J Robust Nonlin Control 13(9):885–907

    MathSciNet  MATH  Google Scholar 

  11. Gilli M (1993) Strange attractors in delayed cellular neural networks. IEEE Trans Circuits Syst 1: Fundam Theory Appl 40(11):849–853

    MathSciNet  MATH  Google Scholar 

  12. Gopalsamy K, He XZ (1994) Stability in asymmetric Hopfield nets with transmission delays. Phys D: Nonlinear Phenom 76(4):344–358

    MathSciNet  MATH  Google Scholar 

  13. Gu Z, Shi P, Yue D, Ding Z (2019) Decentralized adaptive event-triggered \(H_\infty \) filtering for a class of networked nonlinear interconnected systems. IEEE Trans Cybern 49(5):1570–1579

    Google Scholar 

  14. He Y, Ji MD, Zhang CK, Wu M (2016) Global exponential stability of neural networks with time-varying delay based on free-matrix-based integral inequality. Neural Netw 77:80–86

    MATH  Google Scholar 

  15. Karthick SA, Sakthivel R, Wang C, Ma YK (2020) Synchronization of coupled memristive neural networks with actuator saturation and switching topology. Neurocomputing 383:138–150

    Google Scholar 

  16. Liu H, Wang Z, Shen B, Dong H (2020) Delay-distribution-dependent \(H_\infty \) state estimation for discrete-time memristive neural networks with mixed time-delays and fading measurements. IEEE Trans Cybern 50(2):440–451

    Google Scholar 

  17. Li H, Li C, Ouyang D, Nguang SK (2020) Impulsive synchronization of unbounded delayed inertial neural networks with actuator saturation and sampled-data control and its application to image encryption. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.2984770

    Article  Google Scholar 

  18. Li JN, Bao WD, Li SB et al (2016) Exponential synchronization of discrete-time mixed delay neural networks with actuator constraints and stochastic missing data. Neurocomputing 207:700–707

    Google Scholar 

  19. Li X (2010) Global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type. Appl Math Comput 215(12):4370–4384

    MathSciNet  MATH  Google Scholar 

  20. Lian HH, Xiao SP, Yan H, Yang F, Zeng HB (2021) Dissipativity analysis for neural networks with time-varying delays via a delay-product-type Lyapunov functional approach. IEEE Trans Neural Netw Learn Syst 32(3):975–984

    MathSciNet  Google Scholar 

  21. Lin Z (1999) Low gain feedback. Springer, London

    Google Scholar 

  22. Lu H (2002) Chaotic attractors in delayed neural networks. Phys Lett A 298(2–3):109–116

    MATH  Google Scholar 

  23. Ma L, Wang Z, Liu Y, Alsaadi FE (2017) A note on guaranteed cost control for nonlinear stochastic systems with input saturation and mixed time-delays. Int J Robust Nonlin Control 27(18):4443–4456

    MathSciNet  MATH  Google Scholar 

  24. Ma L, Wang Z, Liu Y, Alsaadi FE (2019) Distributed filtering for nonlinear time-delay systems over sensor networks subject to multiplicative link noises and switching topology. Int J Robust Nonlin Control 29(10):2941–2959

    MathSciNet  MATH  Google Scholar 

  25. Mu X, Chen Y (2016) Synchronization of delayed discrete-time neural networks subject to saturated time-delay feedback. Neurocomputing 175:293–299

    Google Scholar 

  26. Ouyang D, Shao J, Jiang H, Nguang SK, Shen HT (2020) Impulsive synchronization of coupled delayed neural networks with actuator saturation and its application to image encryption. Neural Netw 128:158–171

    MATH  Google Scholar 

  27. Pecora LM, Carroll TL, Johnson GA et al (1997) Fundamentals of synchronization in chaotic systems, concepts, and applications. Chaos 7(4):520–543

    MathSciNet  MATH  Google Scholar 

  28. Qian W, Li Y, Zhao Y, Chen Y (2020) New optimal method for \(L_2\)-\(L_\infty \) state estimation of delayed neural networks. Neurocomputing 415:258–265

    Google Scholar 

  29. Qian W, Xing W, Fei S (2020) \(H_\infty \) state estimation for neural networks with general activation function and mixed time-varying delays. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.3016120

    Article  Google Scholar 

  30. Qian W, Li Y, Chen Y, Liu W (2020) \(L_2\)-\(L_\infty \) filtering for stochastic delayed systems with randomly occurring nonlinearities and sensor saturation. Int J Syst Sci 51(13):2360–2377

    Google Scholar 

  31. Selvaraj P, Sakthivel R, Kwon OM (2018) Finite-time synchronization of stochastic coupled neural networks subject to Markovian switching and input saturation. Neural Netw 105:154–165

    MATH  Google Scholar 

  32. Selvaraj P, Sakthivel R, Kwon OM (2018) Synchronization of fractional-order complex dynamical network with random coupling delay, actuator faults and saturation. Nonlinear Dyn 94(4):3101–3116

    MATH  Google Scholar 

  33. Seuret A, Gouaisbaut F (2013) Wirtinger-based integral inequality: application to time-delay systems. Automatica 49(9):2860–2866

    MathSciNet  MATH  Google Scholar 

  34. Sweetha S, Sakthivel R, Harshavarthini S (2021) Finite-time synchronization of nonlinear fractional chaotic systems with stochastic actuator faults. Chaos, Solitons & Fractals 142:110312

    MathSciNet  Google Scholar 

  35. Tarbouriech S, Garcia G, da Silva Gomes JM Jr, Queinnec I (2011) Stability and stabilization of linear systems with saturating actuators. Springer, London

    MATH  Google Scholar 

  36. Tourani S, Rahmani Z, Rezaie B (2016) Adaptive observer-based projective synchronization for chaotic neural networks with mixed time delays. Chin J Phys 54(2):285–297

    MathSciNet  Google Scholar 

  37. Wu ZG, Shi P, Su H, Chu J (2012) Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling. IEEE Trans Neural Netw Learn Syst 23(9):1368–1376

    Google Scholar 

  38. Wu ZG, Shi P, Su H, Chu J (2014) Local synchronization of chaotic neural networks with sampled-data and saturating actuators. IEEE Trans Cybern 44(12):2635–2645

    Google Scholar 

  39. Xiao SP, Lian HH, Teo KL, Zeng HB, Zhang XH (2018) A new Lyapunov functional approach to sampled-data synchronization control for delayed neural networks. J Frankl Inst 355(17):8857–8873

    MathSciNet  MATH  Google Scholar 

  40. Xiong X, Tang R, Yang X (2019) Finite-time synchronization of memristive neural networks with proportional delay. Neural Process Lett 50:1139–1152

    Google Scholar 

  41. Zeng HB, Teo KL, He Y, Xu H, Wang W (2017) Sampled-data synchronization control for chaotic neural networks subject to actuator saturation. Neurocomputing 260:25–31

    Google Scholar 

  42. Zeng HB, Liu XG, Wang W (2019) A generalized free-matrix-based integral inequality for stability analysis of time-varying delay systems. Appl Math Comput 354:1–8

    MathSciNet  MATH  Google Scholar 

  43. Zeng HB, Zhai ZL, Yan H, Wang W (2020) A new looped functional to synchronize neural networks with sampled-data control. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.3027862

    Article  Google Scholar 

  44. Zeng HB, Lin HC, He Y, Teo KL, Wang W (2020) Hierarchical stability conditions for time-varying delay systems via an extended reciprocally convex quadratic inequality. J Frankl Inst 357:9930–9941

    MathSciNet  MATH  Google Scholar 

  45. Zeng HB, Zhai ZL, He Y, Teo KL, Wang W (2020) New insights on stability of sampled-data systems with time-delay. Appl Math Comput 374:374

    MathSciNet  MATH  Google Scholar 

  46. Zhang CK, He Y, Jiang L, Wu M, Wang Q-G (2017) An extended reciprocally convex matrix inequality for stability analysis of systems with time-varying delay. Automatica 85:481–485

    MathSciNet  MATH  Google Scholar 

  47. Zhang CK, Long F, He Y, Yao W, Jiang L, Wu M (2020) A relaxed quadratic function negative-determination lemma and its application to time-delay systems. Automatica 113:108764

    MathSciNet  MATH  Google Scholar 

  48. Zhang X, Yuan Y, Li X (2020) Finite-time stabilization for static neural networks with leakage delay and time-varying delay. Neural Process Lett 51:67–81

    Google Scholar 

  49. Zhang XM, Han QL, Seuret A, Gouaisbaut F (2017) An improved reciprocally convex inequality and an augmented Lyapunov–Krasovskii functional for stability of linear systems with time-varying delay. Automatica 84:221–226

    MathSciNet  MATH  Google Scholar 

  50. Zhang XM, Han QL, Wang Z, Zhang BL (2017) Neuronal state estimation for neural networks with two additive time-varying delay. IEEE Trans Cybern 47(10):3184–3194

    Google Scholar 

  51. Zhang XM, Han QL, Wang J (2018) Admissible delay upper bounds for global asymptotic stability of neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst 29(11):5319–5329

    MathSciNet  Google Scholar 

  52. Zhou B, Lin Z, Duan GR (2010) Global and semi-global stabilization of linear systems with multiple delays and saturations in the input. SIAM J Control Optim 48(8):5294–5332

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant 61773156, the Program for Science and Technology Innovation Talents in the Universities of Henan Province of China under Grant 19HASTIT028, and the Natural Science Foundation of Henan Province of China under Grant 202300410159.

Author information

Authors and Affiliations

  1. Department of Journal Editorial and College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, People’s Republic of China

    Liuyuan Chen

  2. School of Mathematical Science, Henan Institute of Science and Technology, Xinxiang, 453003, People’s Republic of China

    Yonggang Chen & Nannan Zhang

Authors
  1. Liuyuan Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yonggang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nannan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yonggang Chen.

Additional information

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

Chen, L., Chen, Y. & Zhang, N. Synchronization Control for Chaotic Neural Networks with Mixed Delays Under Input Saturations. Neural Process Lett 53, 3735–3755 (2021). https://doi.org/10.1007/s11063-021-10577-9

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-021-10577-9

Keywords

Search

Navigation