Skip to main content
SpringerLink
Log in

Adaptive Synchronization of Complex Dynamical Networks via Distributed Pinning Impulsive Control

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

In this paper, exponential synchronization of a class of nonlinearly coupled complex dynamical networks with time-varying delay is investigated. A novel distributed controller combined with pinning impulsive method is designed by selecting the systems with largest norms of errors to be controlled at every impulsive instant. By introducing the adaptive control protocol into the negative feedback controller, suitable control gains are obtained and therefore, the control cost is efficiently saved. Based on the Lyapunov stability theory and some mathematical techniques, some novel leader-following synchronization criteria are derived. Furthermore, with consideration of time-varying impulsive effects, the obtained results are extended to a more complicated situation. Finally, two numerical examples are performed 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
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Pedarsani R, Walrand J, Zhong Y (2017) Robust scheduling for flexible processing networks. Adv Appl Probab 49:603–628

    MathSciNet  MATH  Google Scholar 

  2. Wang D, Che W, Yu H, Li J (2018) Adaptive pinning synchronization of complex networks with negative weights and its application in traffic road network. Int J Control Autom Syst 16:782–790

    Google Scholar 

  3. Lee C, Chong H, Liao P, Wang X (2017) Critical review of social network analysis applications in complex project management. J Manag Eng 34:1–15

    Google Scholar 

  4. Wang Z, Zhang H (2013) Synchronization stability in complex interconnected neural networks with nonsymmetric coupling. Neurocomputing 108:84–92

    Google Scholar 

  5. Li C, Liu G (2018) Data-driven leader-follower output synchronization for networked non-linear multi-agent systems with switching topology and time-varying delays. J Syst Sci Compl 31:87–102

    MathSciNet  MATH  Google Scholar 

  6. Yang L, Jiang J (2014) Adaptive synchronization of drive-response fractional-order complex dynamical networks with uncertain parameters. Commun Nonlinear Sci Numer Simul 19:1496–1506

    MathSciNet  MATH  Google Scholar 

  7. 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 

  8. Ding K, Han Q (2015) Master-slave synchronization criteria for chaotic hindmarsh-rose neurons using linear feedback control. Complexity 19:73–82

    Google Scholar 

  9. Zhang H, Wang X (2017) Complex projective synchronization of complex-valued neural network with structure identification. J Frankl Inst 354:5011–5025

    MathSciNet  MATH  Google Scholar 

  10. Zhan T, Ma S, Liu X (2019) Synchronization of singular switched complex networks via impulsive control with all nonsynchronized subnetworks. Int J Robust Nonlinear Control 29:4872–4887

    MathSciNet  MATH  Google Scholar 

  11. Zhang W, Yang S, Li C, Li Z (2019) Finite-time and fixed-time synchronization of complex networks with discontinuous nodes via quantized control. Neural Process Lett 50:2073–2086

    Google Scholar 

  12. Ding S, Wang Z, Zhang H (2019) Quasi-synchronization of delayed memristive neural networks via region-partitioning-dependent intermittent control. IEEE Trans Cybern 49:4066–4077

    Google Scholar 

  13. 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 30:1000–1012

    MathSciNet  Google Scholar 

  14. Tang Z, Park JH, Zheng WX (2018) Distributed impulsive synchronization of Lur’e dynamical networks via parameter variation methods. Int J Robust Nonlinear Control 28:1001–1015

    MathSciNet  MATH  Google Scholar 

  15. Wen G, Wang P, Yu X et al (2019) Pinning synchronization of complex switching networks with a leader of nonzero control inputs. IEEE Trans Circuits Syst I Regul Pap 66:3100–3112

    MathSciNet  Google Scholar 

  16. Leng H, Wu Z (2019) Impulsive synchronization of complex-variable network with distributed time delays. Phys A Stat Mech Appl 536:122602

    MathSciNet  Google Scholar 

  17. Perez-Ramos AE, Villarreal-Reyes S, Lepers C et al (2015) Low complexity M-PPM impulse-radio ultra wideband over fiber system for wireless sensor networks applications. IEEJ Trans Electr Electron Eng 10:162–164

    Google Scholar 

  18. Chen T, Liu X, Lu W (2007) Pinning complex networks by a single controller. IEEE Trans Circuits Syst I Regul Pap 54:1317–1326

    MathSciNet  MATH  Google Scholar 

  19. Wang X, Liu X, She K, Zhong S (2017) Pinning impulsive synchronization of complex dynamical networks with various time-varying delay sizes. Nonlinear Anal Hybrid Syst 26:307–318

    MathSciNet  MATH  Google Scholar 

  20. Li H, Hu C, Jiang Y et al (2016) Pinning adaptive and impulsive synchronization of fractional-order complex dynamical networks. Chaos Solitons Fractals 92:142–149

    MathSciNet  MATH  Google Scholar 

  21. Zhou P, Cai S (2017) Pinning synchronization of complex directed dynamical networks under decentralized adaptive strategy for aperiodically intermittent control. Nonlinear Dyn 90:287–299

    MathSciNet  MATH  Google Scholar 

  22. Yang X, Lu J, Ho DWC, Song Q (2018) Synchronization of uncertain hybrid switching and impulsive complex networks. Appl Math Model 59:379–392

    MathSciNet  MATH  Google Scholar 

  23. Ding S, Wang Z (2020) Event-triggered synchronization of discrete-time neural networks: a switching approach. Neural Netw 125:31–40

    MATH  Google Scholar 

  24. Li Z, Fang J, Huang T, Miao Q (2017) Synchronization of stochastic discrete-time complex networks with partial mixed impulsive effects. J Frankl Inst 354:4196–4214

    MathSciNet  MATH  Google Scholar 

  25. Gong X, Wu Z (2015) Adaptive pinning impulsive synchronization of dynamical networks with time-varying delay. Adv Differ Equ 240:1–13

    MathSciNet  MATH  Google Scholar 

  26. Wu Z, Liu D, Ye Q (2015) Pinning impulsive synchronization of complex-variable dynamical network. Commun Nonlinear Sci Numer Simul 20:273–280

    MathSciNet  MATH  Google Scholar 

  27. Lu J, Ho DWC, Cao J (2010) A unified synchronization criterion for impulsive dynamical networks. Automatica 46:1215–1221

    MathSciNet  MATH  Google Scholar 

  28. Yang Z, Xu D (2005) Stability analysis of delay neural networks with impulsive effects. IEEE Trans Circuits Syst Express Briefs 52:517–521

    Google Scholar 

  29. Chen H, Shi P, Lim CC (2018) Pinning impulsive synchronization for stochastic reaction–diffusion dynamical networks with delay. Neural Netw 106:281–293

    MATH  Google Scholar 

  30. Tian Y, Wang Z (2020) Stability analysis for delayed neural networks based on the augmented Lyapunov-Krasovskii functional with delay-product-type and multiple integral terms. Neurocomputing 410:295–303

    Google Scholar 

  31. Zheng S (2012) Adaptive-impulsive projective synchronization of drive-response delayed complex dynamical networks with time-varying coupling. Nonlinear Dyn 67:2621–2630

    MathSciNet  MATH  Google Scholar 

  32. Tian Y, Wang Z (2020) A new multiple integral inequality and its application to stability analysis of time-delay systems. Appl Math Lett 105:106325

    MathSciNet  MATH  Google Scholar 

  33. Yuan M, Luo X, Wang W et al (2019) Pinning synchronization of coupled memristive recurrent neural networks with mixed time-varying delays and perturbations. Neural Process Lett 49:239–262

    Google Scholar 

  34. Tang Z, Park JH, Feng J (2018) Impulsive effects on quasi-synchronization of neural networks with parameter mismatches and time-varying delay. IEEE Trans Neural Netw Learn Syst 29:908–919

    Google Scholar 

  35. Wang J, Ma Q, Chen A, Liang Z (2015) Pinning synchronization of fractional-order complex networks with Lipschitz-type nonlinear dynamics. ISA Trans 57:111–116

    Google Scholar 

  36. Lu J, Kurths J, Cao J et al (2012) Synchronization control for nonlinear stochastic dynamical networks: Pinning impulsive strategy. IEEE Trans Neural Netw Learn Syst 23:285–292

    Google Scholar 

  37. Ahmed MAA, Liu Y, Zhang W, Alsaadi FE (2017) Exponential synchronization via pinning adaptive control for complex networks of networks with time delays. Neurocomputing 225:198–204

    Google Scholar 

  38. Ghaffari A, Arebi S (2016) Pinning control for synchronization of nonlinear complex dynamical network with suboptimal SDRE controllers. Nonlinear Dyn 83:1003–1013

    MathSciNet  MATH  Google Scholar 

  39. Tian Y, Wang Z (2020) \(\text{H}_\infty \) performance state estimation for static neural networks with time-varying delays via two improved inequalities. IEEE Trans Circuits Syst II Express Briefs. https://doi.org/10.1109/tcsii.2020.2995604

  40. Zhou J, Xiang L, Liu Z (2007) Synchronization in complex delayed dynamical networks with impulsive effects. Phys A Stat Mech Appl 384:684–692

    Google Scholar 

  41. Yang X, Lam J, Ho DWC, Feng Z (2017) Fixed-time synchronization of complex networks with impulsive effects via nonchattering control. IEEE Trans Autom Contr 62:5511–5521

    MathSciNet  MATH  Google Scholar 

  42. Tan G, Wang Z (2020) Further result on \(\text{ H}_\infty \) performance state estimation of delayed static neural networks based on an improved reciprocally convex inequality. IEEE Trans Circuits Syst Express Briefs 67:1477–1481

    Google Scholar 

  43. Wang J, Feng J, Xu C, Zhao Y (2012) Cluster synchronization of nonlinearly-coupled complex networks with nonidentical nodes and asymmetrical coupling matrix. Nonlinear Dyn 67:1635–1646

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work were supported by the National Key R&D Program of China with Grant No. 2018YFB1701903, the National Natural Science Foundation of China with Grant No. 61803180, No. 61973138, the 111 Project with Grant No. B12018, and the Natural Science Foundation of Jiangsu Province with Grant No. BK20180599.

Author information

Authors and Affiliations

  1. Engineering Research Center of Internet of Things Technology Applications (Ministry of Education), Jiangnan University, Wuxi, China

    Dong Ding, Ze Tang, Yan Wang & Zhicheng Ji

  2. Department of Electrical Engineering, Yeungnam University, Kyonsan, Republic of Korea

    Ze Tang

Authors
  1. Dong Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ze Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhicheng Ji
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhicheng Ji.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

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

Ding, D., Tang, Z., Wang, Y. et al. Adaptive Synchronization of Complex Dynamical Networks via Distributed Pinning Impulsive Control. Neural Process Lett 52, 2669–2686 (2020). https://doi.org/10.1007/s11063-020-10373-x

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-020-10373-x

Keywords

Search

Navigation