Advertisement

Pinning Impulsive Synchronization of Stochastic Memristor-based Neural Networks with Time-varying Delays

  • Qianhua Fu
  • Jingye Cai
  • Shouming Zhong
  • Yongbin Yu
Regular Papers Intelligent Control and Applications
  • 17 Downloads

Abstract

This paper investigates the exponential and asymptotical synchronization of stochastic memristor-based neural networks (SMNNs) with time-varying delays via pinning impulsive control. A novel type of pinning impulsive controllers is introduced to synchronize the master system and slave system. Based on the physical properties of memristor, the mathematical model of SMNNs is obtained by the theories of drive-response concept, set-valued maps and stochastic differential inclusions. Then some sufficient verifiable conditions are constructed for the synchronization of SMNNs by applying the Lyapunov-Krasovskii functional (LKF) method. Furthermore, some improvements about the proposed control method are also discussed in this paper. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results.

Keywords

Memristor-based neural networks pinning impulsive stochastic synchronization time-varying delays 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    X. F. Hu, S. K. Duan, G. R. Chen, and L. Chen, “Modeling affections with memristor–based associative memory neural networks,” Neurocomputing, vol. 223, pp. 129–137, February 2017.CrossRefGoogle Scholar
  2. [2]
    L. O. Chua, “Memristor–the missing circuit element,” IEEE Transactions on Circuit Theory, vol. 18, no. 5, pp. 507–519, September 1971.CrossRefGoogle Scholar
  3. [3]
    D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, “The missing memristor found,” Nature, vol. 453, no. 7191, pp. 80–83, May 2008.CrossRefGoogle Scholar
  4. [4]
    Q. H. Fu, J. Y. Cai, S. M. Zhong, and Y. B. Yu, “Dissipativity and passivity analysis for memristor–based neural networks with leakage and two additive time–varying delays,” Neurocomputing, vol. 275, pp. 747–757, January 2018.CrossRefGoogle Scholar
  5. [5]
    J. Liu and R. Xu, “Global dissipativity analysis for memristor–based uncertain neural networks with time delay in the leakage term,” International Journal of Control Automation and Systems, vol. 15, no. 5, pp. 2406–2415, October 2017.CrossRefGoogle Scholar
  6. [6]
    J. Cheng, H. Zhu, Y. C. Ding, S. M. Zhong, and Q. S. Zhong, “Stochastic finite–time boundedness for markovian jumping neural networks with time–varying delays,” Applied Mathematics and Computation, vol. 242, pp. 281–295, September 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    J. Cheng, X. H. Chang, H. P. Ju, H. Li, and H. Wang, “Fuzzy–model–based h¥ control for discrete–time switched systems with quantized feedback and unreliable links,” Information Sciences, vol. 436, pp. 181–196, April 2018.MathSciNetCrossRefGoogle Scholar
  8. [8]
    H. J. Freund, “Motor unit and muscle activity in voluntary motor control,” Physiological Reviews, vol. 63, no. 63, pp. 387–436, April 1983.CrossRefGoogle Scholar
  9. [9]
    J. Cheng, H. P. Ju, K. Hamid Reza, and H. Shen, “A flexible terminal approach to sampled–data exponentially synchronization of markovian neural networks with timevarying delayed signals,” IEEE Transactions on Cybernetics, vol. 48, no. 8, pp. 2232–2244, August 2018.CrossRefGoogle Scholar
  10. [10]
    Y. Liu, H. P. Ju, B. Guo, F. Fang, and F. Zhou, “Eventtriggered dissipative synchronization for markovian jump neural networks with general transition probabilities,” International Journal of Robust and Nonlinear Control, pp. 1–16, September 2018.Google Scholar
  11. [11]
    Y. Men, X. Huang, Z. Wang, and H. Shen, “Quantized asynchronous dissipative state estimation of jumping neural networks subject to occurring randomly sensor saturations,” Neurocomputing, vol. 291, pp. 207–214, May 2018.CrossRefGoogle Scholar
  12. [12]
    S. Yang, C. Li, and T. Huang, “Impulsive synchronization for ts fuzzy model of memristor–based chaotic systems with parameter mismatches,” International Journal of Control Automation and Systems, vol. 14, no. 3, pp. 854–864, June 2016.CrossRefGoogle Scholar
  13. [13]
    G. Zhang and Y. Shen, “Exponential synchronization of delayed memristor–based chaotic neural networks via periodically intermittent control,” Neural Networks, vol. 55, pp. 1–10, July 2014.CrossRefzbMATHGoogle Scholar
  14. [14]
    K. Mathiyalagan, H. P. Ju, and R. Sakthivel, “Synchronization for delayed memristive bam neural networks using impulsive control with random nonlinearities,” Applied Mathematics and Computation, vol. 259, no. C, pp. 967–979, May 2015.Google Scholar
  15. [15]
    Z. Cai, L. Huang, and L. Zhang, “New conditions on synchronization of memristor–based neural networks via differential inclusions,” Neurocomputing, vol. 186, pp. 235–250, April 2016.CrossRefGoogle Scholar
  16. [16]
    W. Zhang, C. Li, and T. Huang, “Stability and synchronization of memristor–based coupling neural networks with time–varying delays via intermittent control,” Neurocomputing, vol. 173, no. P3, pp. 1066.1072, January 2016.Google Scholar
  17. [17]
    J. Cheng, H. P. Ju, and J. Cao, “Quantized H¥ filtering for switched linear parameter–varying systems with sojourn probabilities and unreliable communication channels,” Information Sciences, vol. 466, pp. 289–302, October 2018.MathSciNetCrossRefGoogle Scholar
  18. [18]
    J. Cheng, H. Zhu, S. Zhong, and G. Li, “Novel delaydependent robust stability criteria for neutral systems with mixed time–varying delays and nonlinear perturbations,” Applied Mathematics and Computation, vol. 219, no. 14, pp. 7741–7753, March 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    S. Jiao, H. Shen, Y. Wei, X. Huang, and Z. Wang, “Further results on dissipativity and stability analysis of markov jump generalized neural networks with time–varying interval delays,” Applied Mathematics and Computation, vol. 336, pp. 338–350, November 2018.MathSciNetCrossRefGoogle Scholar
  20. [20]
    H. Chen, S. Zhong, X. Liu, Y. Li, and K. Shi, “Improved results on nonlinear perturbed t–s fuzzy system with mixed delays,” Journal of the Franklin Institute, vol. 354, no. 4, pp. 2032–2052, March 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    Y. Liu, H. P. Ju, and F. Fang, “Global exponential stability of delayed neural networks based on a new integral inequality,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, pp. 1–8, 2018.Google Scholar
  22. [22]
    Y. Song and S. Wen, “Synchronization control of stochastic memristor–based neural networks with mixed delays,” Neurocomputing, vol. 156, pp. 121–128, May 2015.CrossRefGoogle Scholar
  23. [23]
    A. Chandrasekar and R. Rakkiyappan, “Impulsive controller design for exponential synchronization of delayed stochastic memristor–based recurrent neural networks,” Neurocomputing, vol. 173, pp. 1348.1355, January 2016.CrossRefGoogle Scholar
  24. [24]
    H. Bao, J. H. Park, and J. Cao, “Exponential synchronization of coupled stochastic memristor–based neural networks with time–varying probabilistic delay coupling and impulsive delay,” IEEE Transactions on Neural Networks and Learning Systems, vol. 27, pp. 190–201, January 2016.MathSciNetCrossRefGoogle Scholar
  25. [25]
    X. Wang, X. Liu, K. She, and S. Zhong, “Pinning impulsive synchronization of complex dynamical networks with various time–varying delay sizes,” Nonlinear Analysis Hybrid Systems, vol. 26, pp. 307–318, November 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    X. Liu, K. Zhang, and W. C. Xie, “Pinning impulsive synchronization of reaction–diffusion neural networks with time–varying delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 5, pp. 1055–1067, May 2017.CrossRefGoogle Scholar
  27. [27]
    X. F. Wang and G. Chen, “Pinning control of scale–free dynamical networks,” Physica A Statistical Mechanics and Its Applications, vol. 310, no. 3, pp. 521–531, July 2002.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    X. Li, X. Wang, and G. Chen, “Pinning a complex dynamical network to its equilibrium,” IEEE Transactions on Circuits and Systems I, vol. 51, no. 10, pp. 2074–2087, October 2004.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    G. Wang and Y. Shen, “Exponential synchronization of coupled memristive neural networks with time delays,” Neural Computing and Applications, vol. 24, no. 6, pp. 1421–1430, May 2014.CrossRefGoogle Scholar
  30. [30]
    Z. Guo, S. Yang, and J. Wang, “Global synchronization of memristive neural networks subject to random disturbances via distributed pinning control,” Neural Networks, vol. 84, pp. 67–79, December 2016.CrossRefGoogle Scholar
  31. [31]
    I. L. Gibbins and J. L. Morris, “Structure of peripheral synapses: autonomic ganglia,” Cell and Tissue Research, vol. 326, no. 2, pp. 205–220, November 2006.CrossRefGoogle Scholar
  32. [32]
    A. Wu, S. Wen, and Z. Zeng, “Synchronization control of a class of memristor–based recurrent neural networks,” Information Sciences, vol. 183, pp. 106–116, January 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    Z. Meng and Z. Xiang, “Stability analysis of stochastic memristor–based recurrent neural networks with mixed time–varying delays,” Neural Computing and Applications, vol. 28, no. 7, pp. 1787–1799, July 2017.CrossRefGoogle Scholar
  34. [34]
    Z. Guo, S. Yang, and J. Wang, “Global synchronization of stochastically disturbed memristive neurodynamics via discontinuous control laws,” IEEE/CAA Journal of Automatica Sinica, vol. 3, no. 2, pp. 121–131, April 2016.MathSciNetCrossRefGoogle Scholar
  35. [35]
    L. Wang, Y. Shen, Q. Yin, and G. Zhang, “Adaptive synchronization of memristor–based neural networks with time–varying delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 9, pp. 2033–2042, September 2015.MathSciNetCrossRefGoogle Scholar
  36. [36]
    J. G. Lu and G. Chen, “Global asymptotical synchronization of chaotic neural networks by output feedback impulsive control: An lmi approach,” Chaos Solitons and Fractals, vol. 41, no. 5, pp. 2293–2300, September 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    H. Chen, S. Peng, and C. C. Lim, “Exponential synchronization for markovian stochastic coupled neural networks of neutral–type via adaptive feedback control,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 7, pp. 1618–1632, July 2016.MathSciNetCrossRefGoogle Scholar
  38. [38]
    F. H. Clarke, R. J. Stem, Y. S. Ledyaev, and R. R. Wolenski “Nonsmooth analysis and control theory,” Graduate Texts in Mathematics, vol. 178, no. 7, pp. 137–151, 1998.MathSciNetGoogle Scholar
  39. [39]
    W. He, F. Qian, and J. Cao, “Pinning–controlled synchronization of delayed neural networks with distributed–delay coupling via impulsive control,” Neural Networks, vol. 85, pp. 1–9, January 2017.CrossRefGoogle Scholar
  40. [40]
    C. Yi, J. Feng, J. Wang, and C. Xu, “Synchronization of delayed neural networks with hybrid coupling via partial mixed pinning impulsive control,” Applied Mathematics and Computation, vol. 312, pp. 78–90, November 2017.MathSciNetCrossRefGoogle Scholar
  41. [41]
    C. Zheng and J. Cao, “Robust synchronization of coupled neural networks with mixed delays and uncertain parameters by intermittent pinning control,” Neurocomputing, vol. 141, no. 4, pp. 153–159, October 2014.CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Qianhua Fu
    • 1
  • Jingye Cai
    • 2
  • Shouming Zhong
    • 2
  • Yongbin Yu
    • 3
  1. 1.School of Information and Software EngineeringUniversity of Electronic Science and Technology of ChinaChengduP. R. China
  2. 2.School of Electrical Engineering and Electronic InformationXihua UniversityChengduP. R. China
  3. 3.School of Mathematical SciencesUniversity of Electronic Science and Technology of ChinaChengduP. R. China

Personalised recommendations