The Intermittent Control Synchronization of Complex-Valued Memristive Recurrent Neural Networks with Time-Delays

Abstract

In this paper, the intermittent control synchronization of complex-valued memristive recurrent neural networks with time-delays is investigated. As a generalization on the real-valued memristive recurrent neural networks, complex-valued memristive recurrent neural networks own more complicated properties. In complex-valued domain, bounded and analytic complex-valued activation functions do not exist. Some assumptions about activation functions in real-valued domain cannot be applied directly to complex-valued fields. By appropriate transformation, complex-valued memristive recurrent neural networks can be divided into real parts and imaginary parts, which can avoid discussing the bounded and analytic. In the framework of differential inclusion theory and Lyapunov method, sufficient criteria of intermittent control synchronization are established. Finally, a simulation is given to verify the validity and feasibility of the sufficient conditions.

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

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

References

  1. 1.

    Chen DC, Zhang YN (2018) Robust zeroing neural-dynamics and its time-varying disturbances suppression model applied to mobile robot manipulators. IEEE Trans Neural Netw Learn Syst 29(9):4385–4397

    Google Scholar 

  2. 2.

    Li S, Zhou MC, Luo X (2018) Modified primal–dual neural networks for motion control of redundant manipulators with dynamic rejection of harmonic noises. IEEE Trans Neural Netw Learn Syst 29(10):4791–4801

    MathSciNet  Google Scholar 

  3. 3.

    Chen DC, Zhang YN (2018) Tracking control of robot manipulators with unknown models: a Jacobian-matrix-adaption method. IEEE Trans Ind Inform 14(7):3044–3053

    Google Scholar 

  4. 4.

    Jankowski S, Lozowski A, Zurada JM (1996) Complex-valued multistate neural associative memory. IEEE Trans Neural Netw 7(6):1491–1496

    Google Scholar 

  5. 5.

    Chen S, Hanzo L, Tan S (2008) Symmetric complex-valued rbf receiver for multiple-antenna aided wireless systems. IEEE Trans Neural Netw 19(9):1659–1665

    Google Scholar 

  6. 6.

    Yu SW, Khwaja AS, Ma JW (2012) Compressed sensing of complex-valued data. Signal Process 92(9):357–362

    Google Scholar 

  7. 7.

    Song QK, Zhao ZJ, Liu YR (2015) Stability analysis of complex-valued neural networks with probabilistic time-varying delays. Neurocomputing 159(1):96–104

    Google Scholar 

  8. 8.

    Zhou C, Zhang W, Yang X, Xu C, Feng J (2017) Finite-time synchronization of complex-valued neural networks with mixed delays and uncertain perturbations. Neural Process Lett 46(1):271–291

    Google Scholar 

  9. 9.

    Wei HZ, Li RX, Chen CR, Tu ZW (2017) Stability analysis of fractional order complex-valued memristive neural networks with time delays. J Frankl Inst 45(2):379–399

    Google Scholar 

  10. 10.

    Chua LO (1971) Memristor-the missing circuit element. IEEE Trans Circuit Theory 18(5):507–519

    Google Scholar 

  11. 11.

    Strukov DB, Snider GS, Stewart DR, Williams RS (2008) The missing memristor found. Nature 453(7191):80–83

    Google Scholar 

  12. 12.

    Liu SX, Yu YG, Zhang S, Zhang YT (2018) Robust stability of fractional-order memristor-based Hopfield neural networks with parameter disturbances. Physica A Stat Mech Appl 509:845–854

    MathSciNet  Google Scholar 

  13. 13.

    Li RX, Cao JD (2016) Stability analysis of reaction–diffusion uncertain memristive neural networks with time-varying delays and leakage term. Appl Math Comput 278:54–69

    MathSciNet  MATH  Google Scholar 

  14. 14.

    Bao HB, Park JH, Cao JD (2015) Matrix measure strategies for exponential synchronization and anti-synchronization of memristor-based neural networks with time-varying delays. Appl Math Comput 270:543–556

    MathSciNet  MATH  Google Scholar 

  15. 15.

    Zhang LZ, Yang YQ, Xu XY (2018) Synchronization analysis for fractional order memristive Cohen–Grossberg neural networks with state feedback and impulsive control. Physica A Stat Mech Appl 506:644–660

    MathSciNet  Google Scholar 

  16. 16.

    Wang HM, Duan SK, Huang TW, Wang LD, Li CD (2017) Exponential stability of complex-valued memristive recurrent neural networks. IEEE Trans Neural Netw Learn Syst 28(3):766–771

    Google Scholar 

  17. 17.

    Shi YC, Cao JD, Chen GR (2017) Exponential stability of complex-valued memristor-based neural networks with time-varying delays. Appl Math Comput 313:222–234

    MathSciNet  MATH  Google Scholar 

  18. 18.

    Li XD, Rakkiyappan R, Velmurugan G (2015) Global dissipativity of memristor-based complex-valued neural networks with time-varying delays. Inf Sci 294:645–665

    MATH  Google Scholar 

  19. 19.

    Velmurugan G, Rakkiyappan R, Lakshmanan S (2014) Passivity analysis of memristor-based complex-valued neural networks with time-varying delays. Neural Process Lett 42(3):517–540

    Google Scholar 

  20. 20.

    Rakkiyappan R, Sivaranjani K, Velmurugan G (2014) Passivity and passification of memristor-based complex-valued recurrent neural networks with interval time-varying delays. Neurocomputing 144:391–407

    Google Scholar 

  21. 21.

    Tan YS, Tang SY, Yang J, Liu ZJ (2017) Robust stability analysis of impulsive complex-valued neural networks with time delays and parameter uncertainties. J Inequal Appl 2017:215

    MathSciNet  MATH  Google Scholar 

  22. 22.

    Chen DC, Zhang YN (2017) A hybrid multi-objective scheme applied to redundant robot manipulators. IEEE Trans Autom Sci Eng 14(3):1337–1350

    Google Scholar 

  23. 23.

    Cantley KD, Subramaniam A, Stiegler HJ, Chapman RA, Vogel EM (2012) Neural learning circuits utilizing nano-crystalline silicon transistors and memristors. IEEE Trans Neural Netw Learn Syst 23(4):565–573

    Google Scholar 

  24. 24.

    Zhang Y, Li S, Liu XP (2018) Neural network-based model-free adaptive near-optimal tracking control for a class of nonlinear systems. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2018.2828114

    Google Scholar 

  25. 25.

    Yang XS, Cao JD (2014) Hybrid adaptive and impulsive synchronization of uncertain complex networks with delays and general uncertain perturbations. Appl Math Comput 227:480–493

    MathSciNet  MATH  Google Scholar 

  26. 26.

    Liang HJ, Zhou Y, Ma H, Wu QH, Yu ZD (2018) Distributed-observer-based output synchronization for heterogeneous double-integral networks. Appl Math Comput 337:535–544

    MathSciNet  Google Scholar 

  27. 27.

    Wen GH, Yu WW, Hu GQ, Cao JD, Yu XH (2015) Pinning synchronization of directed networks with switching topologies: a multiple Lyapunov functions approach. IEEE Trans Neural Netw Learn Syst 26(12):3239–3250

    MathSciNet  Google Scholar 

  28. 28.

    Wu YB, Gao YX, Li WX (2018) Synchronization of stochastic complex networks with time delay via feedback control based on discrete-time state observations. Neurocomputing 315:68–81

    Google Scholar 

  29. 29.

    Wang F, Yang YQ (2018) Intermittent synchronization of fractional order coupled nonlinear systems based on a new differential inequality. Physica A Stat Mech Appl 512:142–152

    MathSciNet  Google Scholar 

  30. 30.

    Yang SJ, Li CD, Huang TW (2016) Exponential stabilization and synchronization for fuzzy model of memristive neural networks by periodically intermittent control. Neural Netw 75:162–172

    MATH  Google Scholar 

  31. 31.

    Feng YM, Yang XS, Song Q, Cao JD (2018) Synchronization of memristive neural networks with mixed delays via quantized intermittent control. Appl Math Comput 339:874–887

    MathSciNet  Google Scholar 

  32. 32.

    Tu ZW, Cao JD, Alsaedi A, Alsaadi FE, Hayat T (2016) Global Lagrange stability of complex-valued neural networks of neutral type with time-varying delays. Complexity 21(S2):438–450

    MathSciNet  Google Scholar 

  33. 33.

    Liu D, Zhu S, Sun KL (2018) New results for exponential stability of complex-valued memristive neural networks with variable delays. Neurocomputing 275:758–767

    Google Scholar 

  34. 34.

    Wang H, Duan S, Huang T, Wang L, Li C (2017) Exponential stability of complex-valued memristive recurrent neural networks. IEEE Trans Neural Netw Learn Syst 28(3):766–771

    Google Scholar 

  35. 35.

    Rakkiyappan R, Velmurugan G, Cao JD (2014) Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays. Nonlinear Dyn 78(4):2823–2836

    MathSciNet  MATH  Google Scholar 

  36. 36.

    Liu D, Zhu S, Sun KL (2018) Anti-synchronization of complex-valued memristor-based delayed neural networks. Neural Netw 105:1–13

    Google Scholar 

  37. 37.

    Guo YX (2013) Mean square exponential stability of stochastic delay cellular neural networks. Electron J Qual Theory Differ Equ 16(34):1–10

    MathSciNet  MATH  Google Scholar 

  38. 38.

    Li M, Wang J (2018) Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differentisal equations. Appl Math Comput 324:254–265

    MathSciNet  MATH  Google Scholar 

  39. 39.

    Li YN, Sun YG, Meng FW (2017) New criteria for exponential stability of switched time varying systems with delays and nonlinear disturbances. Nonlinear Anal Hybrid Syst 26:284–291

    MathSciNet  MATH  Google Scholar 

  40. 40.

    Zhang H, Ye M, Ye Renyu, Cao JD (2018) Synchronization stability of Riemann-Liouville fractional delay-coupled complex neural networks. Physica A Stat Mech Appl 508:155–165

    MathSciNet  Google Scholar 

  41. 41.

    Yu ZY, Jiang HJ, Hu C, Fan XL (2016) Consensus of second-order multi-agent systems with delayed nonlinear dynamics and aperiodically intermittent communications. Int J Control 90(5):909–922

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Yongqing Yang.

Additional information

Publisher's Note

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

This work was jointly supported by the Natural Science Foundation of Jiangsu Province of China under Grant No. BK20161126, BK20170171, Postgraduate Research & Practice Innovation Program of Jiangsu Province under Grant Nos. KYCX18_1857, KYCX18_1858.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhang, S., Yang, Y. & Sui, X. The Intermittent Control Synchronization of Complex-Valued Memristive Recurrent Neural Networks with Time-Delays. Neural Process Lett 50, 2119–2139 (2019). https://doi.org/10.1007/s11063-019-09988-6

Download citation

Keywords

  • Complex-valued recurrent neural networks
  • Memeristor
  • Synchronization
  • Intermittent control
  • Differential inclusion
  • Time-delays