Skip to main content

Advertisement

SpringerLink
Log in

Synchronization of coupled neural networks with infinite-time distributed delays via quantized intermittent pinning control

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

A Correction to this article was published on 30 July 2018

This article has been updated

Abstract

How to deal with the effect of infinite-time delay and maximize rest width is the main difficulty for intermittent control techniques. This paper considers asymptotic synchronization of coupled neural networks (CNNs) with bounded time-varying discrete delay and infinite-time distributed delay (mixed delays). A quantized intermittent pinning control scheme is designed to save both channel resources and control cost and reduce both the amount of transmitted information and channel blocking. Two weighted integral inequalities are first established to deal with the infinite-time distributed delay. Based on weighted double-integral inequalities, novel Lyapunov–Krasovskii functionals with negative terms are designed, which can reduce the conservativeness of the results. Some sufficient conditions in the form of linear matrix inequalities are obtained to ensure that the CNNs asymptotically synchronize to an isolated system. Moreover, the relationships between the control width, rest width, and convergence rate are explicitly given. Furthermore, an optimal algorithm is provided to increase the rest width as large as possible. As special cases, the synchronization of the CNNs with quantized pinning control and quantized intermittent control are also considered, respectively. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

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

Similar content being viewed by others

Change history

  • 30 July 2018

    The third author’s name was incomplete and incorrect in the original publication.

References

  1. Shi, L., Yang, X., Li, Y., Feng, Z.: Finite-time synchronization of nonidentical chaotic systems with multiple time-varying delays and bounded perturbations. Nonlinear Dyn. 83(1–2), 75–87 (2016)

    Article  MathSciNet  Google Scholar 

  2. Farivar, F., Shoorehdeli, M.A.: Fault tolerant synchronization of chaotic heavy symmetric gyroscope systems versus external disturbances via Lyapunov rule-based fuzzy control. ISA Trans. 51, 50–64 (2012)

    Article  Google Scholar 

  3. Cheng, J., Park, J.H., Zhang, L., Zhu, Y.: An asynchronous operation approach to event-triggered control for fuzzy Markovian jump systems with general switching policies. IEEE Trans. Fuzzy Syst. 26(1), 6–18 (2018)

    Article  Google Scholar 

  4. Wu, E., Yang, X.: Adaptive synchronization of coupled nonidentical chaotic systems with complex variables and stochastic perturbations. Nonlinear Dyn. 84(1), 261–269 (2016)

    Article  MathSciNet  Google Scholar 

  5. Yang, X., Lu, J.: Finite-time synchronization of coupled networks with Markovian topology and impulsive effects. IEEE Trans. Autom. Control 61(8), 2256–2261 (2016)

    Article  MathSciNet  Google Scholar 

  6. Zhang, S., Meng, X., Zhang, T.: Dynamics analysis and numerical simulations of a stochastic non-autonomous predator-prey system with impulsive effects. Nonlinear Anal. Hybrid Syst. 26, 19–37 (2017)

    Article  MathSciNet  Google Scholar 

  7. Yang, X., Lam, J., Ho, D.W.C.: Fixed-time synchronization of complex networks with impulsive effects via non-chattering control. IEEE Trans. Autom. Control 62(11), 5511–5521 (2018)

    Article  Google Scholar 

  8. Li, H., Liao, X., Huang, T., Wang, Y., Han, Q., Dong, T.: Algebraic criteria for second-order global consensus in multi-agent networks with intrinsic nonlinear dynamics and directed topologies. Inf. Sci. 259, 25–35 (2014)

    Article  MathSciNet  Google Scholar 

  9. Xu, C., Yang, X., Lu, J., Feng, J. Alsaadi, F.E., Hayat, T.: Finite-time synchronization of networks via quantized intermittent pinning control, IEEE Trans. Cybern. https://doi.org/10.1109/TCYB.2017.2749248

    Article  Google Scholar 

  10. Wang, J.-L., Wu, H.-N., Huang, T., Ren, S.-Y.: Pinning control strategies for synchronization of linearly coupled neural networks with reaction–diffusion terms. IEEE Trans. Neural Netw. Learn. Syst. 27(4), 749–761 (2016)

    Article  MathSciNet  Google Scholar 

  11. Mobayen, S., Tchier, F.: Composite nonlinear feedback control technique for master/slave synchronization of nonlinear systems. Nonlinear Dyn. 87(3), 1731–1747 (2017)

    Article  Google Scholar 

  12. Gout, J., Quade, M., Shafi, K., Niven, R.K., Abel, M.: Synchronization control of oscillator networks using symbolic regression. Nonlinear Dyn. 91(2), 1001–1021 (2018)

    Article  Google Scholar 

  13. Tang, Y., Gao, H., Zhang, W., Kurths, J.: Leader-following consensus of a class of stochastic delayed multi-agent systems with partial mixed impulses. Automatica 53, 346–354 (2015)

    Article  MathSciNet  Google Scholar 

  14. Wang, B., Yan, J., Cheng, J., Zhong, S.: New criteria of stability analysis for generalized neural networks subject to time-varying delayed signals. Appl. Math. Comput. 314, 322–333 (2017)

    MathSciNet  Google Scholar 

  15. Wang, Y., Cao, J., Hu, J.: Stochastic synchronization of coupled delayed neural networks with switching topologies via single pinning impulsive control. Neural Comput. Appl. 26(7), 1739–1749 (2015)

    Article  Google Scholar 

  16. Liu, Y., Guo, B.-Z., Park, J.H., Lee, S.-M.: Nonfragile exponential synchronization of delayed complex dynamical networks with memory sampled-data control. IEEE Trans. Neural Netw. Learn. Syst. 29(1), 118–128 (2018)

    Article  MathSciNet  Google Scholar 

  17. Wu, Y., Cao, J., Li, Q., Alsaedi, A., Alsaadi, F.E.: Finite-time synchronization of uncertain coupled switched neural networks under asynchronous switching. IEEE Trans. Cybern. 85, 128–139 (2017)

    Google Scholar 

  18. Yang, X., Feng, Z., Feng, J., Cao, J.: Synchronization of discrete-time neural networks with delays and Markov jump topologies based on tracker information. Neural Netw. 85, 157–164 (2017)

    Article  Google Scholar 

  19. Yang, X., Ho, D .W .C.: Synchronization of delayed memristive neural networks: robust analysis approach. IEEE Trans. Cybern. 46(12), 3377–3387 (2016)

    Article  Google Scholar 

  20. Sakthivel, R., Anbuvithya, R., Mathiyalagan, K., Ma, Y.-K., Prakash, P.: Reliable anti-synchronization conditions for BAM memristive neural networks with different memductance functions. Appl. Math. Comput. 275, 213–228 (2016)

    MathSciNet  Google Scholar 

  21. Mathiyalagan, K., Anbuvithya, R., Sakthivel, R., Park, J.H., Prakash, P.: Non-fragile \(H_{\infty }\) synchronization of memristor-based neural networks using passivity theory. Neural Netw. 74, 85–100 (2016)

    Article  Google Scholar 

  22. Zhang, H., Wang, J., Wang, Z., Liang, H.: Sampled-data synchronization analysis of Markovian neural networks with generally incomplete transition rates. IEEE Trans. Neural Netw. Learn. Syst 28(3), 740–752 (2017)

    Article  MathSciNet  Google Scholar 

  23. Yang, X., Cao, J., Liang, J.: Exponential synchronization of memristive neural networks with delays: Interval matrix method. IEEE Trans. Neural Netw. Learn. Syst. 28(8), 1878–1888 (2017)

    Article  MathSciNet  Google Scholar 

  24. Zhang, L., Zhu, Y., Zheng, W.X.: Synchronization and state estimation of a class of hierarchical hybrid neural networks with time-varying delays, IEEE Trans. Neural Netw. Learn. Syst. 27(2), 459–470 (2016)

    Article  MathSciNet  Google Scholar 

  25. Anbuvithya, R., Mathiyalagan, K., Sakthivel, R., Prakash, P.: Non-fragile synchronization of memristive BAM networks with random feedback gain fluctuations. Commun. Nonlinear Sci. Numer. Simul. 29, 427–440 (2015)

    Article  MathSciNet  Google Scholar 

  26. Zhang, W., Li, C., Huang, T., Xiao, M.: Synchronization of neural networks with stochastic perturbation via aperiodically intermittent control. Neural Netw. 71, 105–111 (2015)

    Article  Google Scholar 

  27. Cheng, J., Park, J.H., Liu, Y., et al.: Finite-time \(H_{\infty }\) fuzzy control of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions. Fuzzy Sets Syst. 314, 99–115 (2017)

    Article  Google Scholar 

  28. Hu, C., Yu, J., Jiang, H., Teng, Z.: Exponential lag synchronization for neural networks with mixed delays via periodically intermittent control. Chaos 20, 023108 (2010)

    Article  MathSciNet  Google Scholar 

  29. Liu, Y., Park, J. H., Fang, F.: Global exponential stability of delayed neural networks based on a new integral inequality. IEEE Trans. Syst. Man Cybern. Syst. https://doi.org/10.1109/TSMC.2018.2815560

  30. Chen, W.-H., Liu, L., Lu, X.: Intermittent synchronization of reaction-diffusion neural networks with mixed delays via razumikhin technique. Nonlinear Dyn. 87, 535–551 (2017)

    Article  Google Scholar 

  31. Song, Q., Huang, T.: Stabilization and synchronization of chaotic systems with mixed time-varying delays via intermittent control with non-fixed both control period and control width. Neurocomputing 154, 61–69 (2015)

    Article  Google Scholar 

  32. Hu, C., Jiang, H., Teng, Z.: Impulsive control and synchronization for delayed neural networks with reaction–diffusion terms. IEEE Trans. Neural Netw. 21(1), 67–81 (2010)

    Article  Google Scholar 

  33. Yang, X.: Can neural networks with arbitrary delays be finite-timely synchronized? Neurocomputing 143, 275–281 (2014)

    Article  Google Scholar 

  34. Liu, Y., Wang, Z., Liang, J., Liu, X.: Synchronization of coupled neutral-type neural networks with jumping-mode-dependent discrete and unbounded distributed delays. IEEE Trans. Cybern. 43(1), 102–114 (2013)

    Article  Google Scholar 

  35. Halanay, A.: Differential Equations: Stability, Oscillations, Time Lags. Academic, San Diego, CA (1966)

    MATH  Google Scholar 

  36. Sorrentino, F., Bernardo, M d, Garofalo, F., Chen, G.: Controllability of complex networks via pinning. Phys. Rev. E 75(4), 046103 (2007)

    Article  Google Scholar 

  37. Zhou, J., Wu, X., Small, M., Lu, J.: Pinning synchronization of delayed neural networks. Chaos 18, 043111 (2008)

    Article  MathSciNet  Google Scholar 

  38. Song, Q., Cao, J.: On pinning synchronization of directed and undirected complex dynamical networks. IEEE Trans. Circ. Syst. I 57(3), 672–680 (2010)

    MathSciNet  Google Scholar 

  39. Song, Q., Cao, J., Liu, F.: Pinning-controlled synchronization of hybrid-coupled complex dynamical networks with mixed time-delays. Int. J. Robust Nonlinear Control 22(6), 690–706 (2012)

    Article  MathSciNet  Google Scholar 

  40. Yang, X., Cao, J.: Adaptive pinning synchronization of coupled neural networks with mixed delays and vector-form stochastic perturbations. Acta Math. Sci. 32B(3), 955–977 (2012)

    MathSciNet  MATH  Google Scholar 

  41. Wen, G., Yu, W., Hu, G., Cao, J., Yu, X.: Pinning synchronization of directed networks with switching topologies: A multiple lyapunov functions approach. IEEE Trans. Neural Netw. Learn. Syst. 26(12), 3239–3250 (2015)

    Article  MathSciNet  Google Scholar 

  42. Lu, J., Zhong, J., Huang, C., Cao, J.: On pinning controllability of boolean control networks. IEEE Trans. Autom. Control 61(6), 1658–1663 (2016)

    Article  MathSciNet  Google Scholar 

  43. He, W., Qian, F., Cao, J.: Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control. Neural Networks 85, 1–9 (2017)

    Article  Google Scholar 

  44. Dharani, S., Rakkiyappan, R., Park, J.H.: Pinning sampled-data synchronization of coupled inertial neural networks with reaction-diffusion terms and time-varying delays. Neurocomputing 227, 101–107 (2017)

    Article  Google Scholar 

  45. Liu, X., Chen, T.: Synchronization of complex networks via aperiodically intermittent pinning control. IEEE Trans. Autom. Control 60(12), 3316–3321 (2015)

    Article  MathSciNet  Google Scholar 

  46. Wang, J., Feng, J., Xu, C., Zhao, Y.: Exponential synchronization of stochastic perturbed complex networks with time-varying delays via periodically intermittent pinning. Commun. Nonlinear Sci. Numer. Simul. 18(11), 3146–3157 (2013)

    Article  MathSciNet  Google Scholar 

  47. Cai, S., Zhou, P., Liu, Z.: Intermittent pinning control for cluster synchronization of delayed heterogeneous dynamical networks. Nonlinear Anal. Hybrid Syst. 18, 134–155 (2015)

    Article  MathSciNet  Google Scholar 

  48. Liu, X., Chen, T.: Synchronization of linearly coupled networks with delays via aperiodically intermittent pinning control. IEEE Trans. Neural Netw. Learn. Syst. 26(10), 2396–2407 (2015)

    Article  MathSciNet  Google Scholar 

  49. Feng, J., Yang, P., Zhao, Y.: Cluster synchronization for nonlinearly time-varying delayed coupling complex networks with stochastic perturbation via periodically intermittent pinning control. Appl. Math. Comput. 291, 52–68 (2016)

    MathSciNet  Google Scholar 

  50. Brockett, R.W., Liberzon, D.: Quantized feedback stabilization of linear systems. IEEE Trans. Autom. Control 45(7), 1279–1289 (2000)

    Article  MathSciNet  Google Scholar 

  51. Liberzon, D.: Hybrid feedback stabilization of systems with quantized signals. Automatica 39, 1543–1554 (2003)

    Article  MathSciNet  Google Scholar 

  52. Fagnani, F., Zampieri, S.: Stability analysis and synthesis for scalar linear systems with a quantized feedback. IEEE Trans. Autom. Control 48(9), 1569–1584 (2003)

    Article  MathSciNet  Google Scholar 

  53. Liu, W., Wang, Z., Ni, M.: Quantized feedback stabilization for a class of linear systems with nonlinear disturbances. Nonlinear Anal. Hybrid Syst. 8, 48–56 (2013)

    Article  MathSciNet  Google Scholar 

  54. Song, G., Li, T., Li, Y., Lu, J.: Quantized output feedback stabilization for nonlinear discrete-time systems subject to saturating actuator. Nonlinear Dyn. 83(1), 305–317 (2016)

    Article  MathSciNet  Google Scholar 

  55. Liu, Z., Wang, F., Zhang, Y., Chen, C.L.P.: Fuzzy adaptive quantized control for a class of stochastic nonlinear uncertain systems. IEEE Trans. Cybern. 46(2), 524–534 (2016)

    Article  Google Scholar 

  56. Yang, X., Cao, J., Xu, C., Feng, J.: Finite-time stabilization of switched dynamical networks with quantized couplings via quantized controller. Sci. China Tech. Sci. 61(2), 299–308 (2018)

    Article  Google Scholar 

  57. Filippov, A.: Differential equations with discontinuous righthand sides. Kluwer Academic Publisher, Dordrecht (1988)

    Book  Google Scholar 

  58. Aubin, J.-P., Cellina, A.: Differential Inclusions: Set-Valued Maps and Viability Theory, vol. 264. Springer, Berlin (2012)

    MATH  Google Scholar 

  59. Horn, R., Johnson, C.: Matrix Analysis. Cambridge University Press, Cambridge University Press (1990)

    MATH  Google Scholar 

  60. Hien, L.V., Trinh, H.: Exponential stability of time-delay systems via new weighted integral inequalities. Appl. Math. Comput. 275, 335–344 (2016)

    MathSciNet  Google Scholar 

  61. Boyd, S., Ghaoui, L.El, Feron, E., Balakrishnan, V.: Linear matrix inequalities in system and control theory. SIAM, Philadelphia (1994)

    Book  Google Scholar 

  62. Wang, T., Xie, L., de Souza, C.: Robust control of a class of uncertain nonlinear systems. Syst. Control Lett. 19(2), 139–149 (1992)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was jointly supported by the National Natural Science Foundation of China (NSFC) under Grants Nos. 61673078 and 61773155, the program of Bowang Scholar of Chongqing Normal University, Scientific and Technological Research Foundation of Chongqing Municipal Education Commission (Grant No. KJ1710253), Program of Chongqing Municipal Key Laboratory of Institutions of Higher Education (Grant No. [2017]3), Program of Chongqing Development and Reform Commission (Grant No. 2017[1007]). The authors declare that there are no conflicts of interest or financial disclosures relevant to this manuscript.

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    Xinsong Yang

  2. Key Laboratory of Intelligent Information Processing and Control of Chongqing Municipal Institutions of Higher Education, Chongqing, 404100, China

    Yuming Feng

  3. Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China

    Ka Fai Cedric Yiu

  4. College of Electrical Engineering, Henan University of Technology, Zhengzhou, 450001, China

    Qiang Song

  5. Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Fuad E. Alsaadi

Authors
  1. Xinsong Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuming Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ka Fai Cedric Yiu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qiang Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Fuad E. Alsaadi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xinsong Yang.

Additional information

The original version of this article was revised: The third author’s name has been corrected.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, X., Feng, Y., Yiu, K.F.C. et al. Synchronization of coupled neural networks with infinite-time distributed delays via quantized intermittent pinning control. Nonlinear Dyn 94, 2289–2303 (2018). https://doi.org/10.1007/s11071-018-4449-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-018-4449-x

Keywords

Search

Navigation