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Synchronization of Multi-links Memristor-Based Switching Networks Under Uniform Random Attacks

  • Baolin Qiu
  • Lixiang Li
  • Haipeng Peng
  • Yixian Yang
Article

Abstract

A variety of influence factors are common to the support networks which are used as cyber-physical systems. In this paper, we consider the problem of finite-time and exponential synchronization for the memristor-based switching networks (MSNs) with multi-links and multiple time-varying delays under uniform random attacks via asymptotic controller and adaptive controller. We propose a more general system model and utilize an analytical method which is different from the classical analytical techniques like set-valued mappings technique and differential inclusions to preprocess the MSNs to a class of switching networks with some uncertain parameters. Then, based on appropriate Lyaponov functionals and linear matrix inequality, several useful criteria ensuring the finite-time synchronization or asymptotic synchronization of MSNs with multi-links and time-varying delays under uniform random attacks via designed control law are obtained. Finally, two numerical examples are designed to show the feasibility and the correctness of our proposed results.

Keywords

Finite-time and exponential synchronization Memristor-based switching networks Multi-links Uniform random attacks Adaptive controller 

Notes

Acknowledgements

The authors would like to thank all the editor as well as the anonymous reviewers for their constructive suggestions, which are important and helpful to improve the quality of this paper. The work is supported by the National Key Research and Development Program (Grant No. 2016YFB0800602) and the National Natural Science Foundation of China (Grant Nos. 61472045, 61573067, 61771071).

References

  1. 1.
    Chua LO (1971) Memristor-the missing circuit element. IEEE Trans Circuit Theory 18:507–519CrossRefGoogle Scholar
  2. 2.
    Soudry D, Di CD, Gal A, Kolodny A, Kvatinsky S (2015) Memristor-based multilayer neural networks with online gradient descent training. IEEE Trans Neural Netw Learn Syst 26(10):2408–2421MathSciNetCrossRefGoogle Scholar
  3. 3.
    Velmurugan G, Rakkiyappan R, Cao J (2016) Finite-time synchronization of fractional-order memristor-based neural networks with time delays. Nonlinear Dyn 73:36–46MATHGoogle Scholar
  4. 4.
    Abdurahman A, Jiang H, Rahman K (2015) Function projective synchronization of memristor-based Cohen–Grossberg neural networks with time-varying delays. Cognit Neurodyn 9(6):603–613CrossRefGoogle Scholar
  5. 5.
    Zhang W, Li C, Huang T, He X (2015) Synchronization of memristor-based coupling recurrent neural networks with time-varying delays and impulses. IEEE Trans Neural Netw Learn Syst 26(12):3308–3313MathSciNetCrossRefGoogle Scholar
  6. 6.
    Guo Z, Wang J, Yan Z (2015) Global exponential synchronization of two memristor-based recurrent neural networks with time delays via static or dynamic coupling. IEEE Trans Syst Man Cybern Syst 45(2):235–249CrossRefGoogle Scholar
  7. 7.
    Chen L, Liu C, Wu R, He Y, Chai Y (2016) Finite-time stability criteria for a class of fractional-order neural networks with delay. Neural Comput Appl 27(3):549–556CrossRefGoogle Scholar
  8. 8.
    Wu X, Liu Y, Zhou J (2015) Pinning adaptive synchronization of general time-varying delayed and multi-linked networks with variable structures. Neurocomputing 147:492–499CrossRefGoogle Scholar
  9. 9.
    Wu A, Wen S, Zeng Z (2014) Synchronization control of a class of memristor-based recurrent neural networks. Neural Netw 63(1):133–140Google Scholar
  10. 10.
    Shi K, Liu X, Zhu H et al (2016) Novel integral inequality approach on master-slave synchronization of chaotic delayed Lur’e systems with sampled-data feedback control. Nonlinear Dyn 83(3):1259–1274MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Zheng M, Li L, Peng H, Xiao J, Yang Y, Zhao H (2016) Finite-time stability and synchronization for memristor-based fractional-order Cohen–Grossberg neural network. Eur Phys J B 89:204.  https://doi.org/10.1140/epjb/e2016-70337-6MathSciNetCrossRefGoogle Scholar
  12. 12.
    Mathiyalagan K, Anbuvithya R, Sakthivel R, Park J, Prakash P (2016) Non-fragile H\(\infty \) synchronization of memristor-based neural networks using passivity theory. Neural Netw 74:85–100CrossRefGoogle Scholar
  13. 13.
    Yang X, Ho DWC (2015) Synchronization of delayed memristive neural networks: robust analysis approach. IEEE Trans Cybern 46(12):3377–3387CrossRefGoogle Scholar
  14. 14.
    Wu H, Zhang L, Ding S, Guo X, Wang L (2013) Complete periodic synchronization of memristor-based neural networks with time-varying delays. Discret Dyn Nat Soc 11:479–504MathSciNetGoogle Scholar
  15. 15.
    Wang G, Shen Y (2014) Exponential synchronization of coupled memristive neural networks with time delays. Neural Comput Appl 24(6):1421–1430CrossRefGoogle Scholar
  16. 16.
    Ding S, Wang Z (2015) Stochastic exponential synchronization control of memristive neural networks with multiple time-varying delays. Neurocomputing 162:16–25CrossRefGoogle Scholar
  17. 17.
    Chandrasekar A, Rakkiyappan R (2016) Impulsive controller design for exponential synchronization of delayed stochastic memristor-based recurrent neural networks. Neurocomputing 173(P3):1348–1355CrossRefGoogle Scholar
  18. 18.
    Wang W, Li L, Peng H et al (2016) Finite-time anti-synchronization control of memristive neural networks with stochastic perturbations. Neural Process Lett 43(1):49–63CrossRefGoogle Scholar
  19. 19.
    Wang W, Li L, Peng H et al (2015) Anti-synchronization of coupled memristive neutral-type neural networks with mixed time-varying delays via randomly occurring control. Nonlinear Dyn 83(4):2143–2155MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Zhao H, Li L, Peng H et al (2015) Anti-synchronization for stochastic memristor-based neural networks with non-modeled dynamics via adaptive control approach. Eur Phys J B 88(5):1–10MathSciNetCrossRefGoogle Scholar
  21. 21.
    Bao H, Ju HP, Cao J (2015) Adaptive synchronization of fractional-order memristor-based neural networks with time delay. Nonlinear Dyn 82(3):1–12MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Chandrasekar A, Rakkiyappan R, Cao J, Lakshmanan S (2014) Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach. Neural Netw 57(9):79–93CrossRefMATHGoogle Scholar
  23. 23.
    Wang LC, Chen S, Li X (2015) Adaptive synchronization of memristor-based neural networks with time-varying delays. Neurocomputing 147(1):2033–2042MathSciNetGoogle Scholar
  24. 24.
    Zhang G, Shen Y (2015) Exponential stabilization of memristor-based chaotic neural networks with time-varying delays via intermittent control. IEEE Trans Neural Netw Learn Syst 26(7):1431–1441MathSciNetCrossRefGoogle Scholar
  25. 25.
    Zhang W, Li C, Huang T, Tan J (2015) Exponential stability of inertial BAM neural networks with time-varying delay via periodically intermittent control. Neural Computing and Applications 26(7):1781–1787CrossRefGoogle Scholar
  26. 26.
    Guo Z, Yang S, Wang J (2016) Global synchronization of memristive neural networks subject to random disturbances via distributed pinning control. Neural Netw 84:67–79CrossRefGoogle Scholar
  27. 27.
    Institute of Curriculum and Teaching Materials (2015) Biological compulsory course 3: the steady state and environment. People’s Education Press, BeijingGoogle Scholar
  28. 28.
    Wang W, Li L, Peng H, Kurths J, Xiao J, Yang Y (2016) Finite-time anti-synchronization control of memristive neural networks with stochastic perturbations. Neural Process Lett 43(1):49–63CrossRefGoogle Scholar
  29. 29.
    Yang x, Cao j, Liang J (2016) Exponential synchronization of memristive neural networks with delays: interval matrix method. IEEE Trans Neural Netw Learn Syst 99:1–11Google Scholar
  30. 30.
    Wei H, Li R, Chen C, Tu Z (2017) Sampled-data state estimation for delayed memristive neural networks with reaction-diffusion terms: Hardy–Poincare inequality. Neurocomputing  https://doi.org/10.1016/j.neucom.2017.05.060
  31. 31.
    Li R, Cao J, Alsaedi A, Hayat T (2017) Non-fragile state observation for delayed memristive neural networks: continuous-time case and discrete-time case. Neurocomputing 245:102–113CrossRefGoogle Scholar
  32. 32.
    Li R, Cao J (2017) Finite-Time and Fixed-Time Stabilization Control of Delayed Memristive Neural Networks: Robust Analysis Technique. Neural Process Lett.  https://doi.org/10.1007/s11063-017-9689-0
  33. 33.
    Abdurahman A, Jiang H, Teng Z (2015) Finite-time synchronization for memristor-based neural networks with time-varying delays. Neural Netw 69:20–28CrossRefGoogle Scholar
  34. 34.
    Mei J, Jiang M, Wang B, Long B (2013) Finite-time parameter identification and adaptive synchronization between two chaotic neural networks. J Frankl Inst 350:1617–1633MathSciNetCrossRefMATHGoogle Scholar
  35. 35.
    Boyd S, Ghaoui LE, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, PhiladelphiaCrossRefMATHGoogle Scholar
  36. 36.
    Tang Y (1998) Terminal sliding mode control for rigid robots. Automatica 34:51–56MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    Wang J, Jian J, Yan P (2009) Finite-time boundedness analysis of a class of neutral type neural networks with time delays. ISNN 2009. Part I, LNCS 5551:395–404Google Scholar
  38. 38.
    Mao X (2002) A note on the LaSalle-type theorems for stochastic differential delay equations. J Math Anal Appl 268:125–142MathSciNetCrossRefMATHGoogle Scholar
  39. 39.
    ksendal B (2005) Stochastic differential equation C an introduction with applications. Springer, New YorkGoogle Scholar
  40. 40.
    Li N, Cao J (2016) Lag synchronization of memristor-based coupled neural networks via \(\omega \)-measure. IEEE Trans Neural Netw Learn Syst 27(3):686–697MathSciNetCrossRefGoogle Scholar
  41. 41.
    Chen C, Li L, Peng H et al (2017) Finite-time synchronization of memristor-based neural networks with mixed delays. Neurocomputing 235:83–89CrossRefGoogle Scholar
  42. 42.
    Abdurahman A, Jiang H, Teng Z (2016) Exponential lag synchronization for memristor-based neural networks with mixed time delays via hybrid switching control. J Frankl Inst 353(13):2859–2880MathSciNetCrossRefMATHGoogle Scholar
  43. 43.
    Tang Z, Park J H, Shen H (2017) Finite-time cluster synchronization of Lur’e networks: a nonsmooth approach. IEEE Trans Syst Man Cybern Syst.  https://doi.org/10.1109/TSMC.2017.2657779
  44. 44.
    Liu X, Park JH, Jiang N, Cao J (2014) Nonsmooth finite-time stabilization of neural networks with discontinuous activations. Neural Netw 52:25–32CrossRefMATHGoogle Scholar
  45. 45.
    Aghababa MP, Khanmohammadi S, Alizadeh G (2011) Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique. Appl Math Model 35(6):3080–3091MathSciNetCrossRefMATHGoogle Scholar
  46. 46.
    Tang Z, Park JH, Feng J (2017) Impulsive effects on quasi-synchronization of neural networks with parameter mismatches and time-varying delay. IEEE Trans Neural Netw Learn Syst.  https://doi.org/10.1109/TNNLS.2017.2651024

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Information Security Center, State Key Laboratory of Networking and Switching TechnologyBeijing University of Posts and TelecommunicationsBeijingChina
  2. 2.National Engineering Laboratory for Disaster Backup and RecoveryBeijing University of Posts and TelecommunicationsBeijingChina

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