Advertisement

On Impulsive Synchronization Control for Coupled Inertial Neural Networks with Pinning Control

  • Tianhu Yu
  • Huamin Wang
  • Jinde CaoEmail author
  • Yang Yang
Article

Abstract

The impulsive control for the synchronization problem of coupled inertial neural networks involved distributed-delay coupling is investigated in the present paper. A novel impulsive pinning control method is introduced to obtain the complete synchronization of the coupled inertial neural networks with three different coupling structures. At each impulsive control instant, the pinning-controlled nodes can be selected according to our selection strategy which is dependent on the lower bound of the pinning control ratio. Our criteria can be utilized to declare the synchronization of the coupled neural networks with asymmetric and reducible coupling structures. The effectiveness of our control strategy is exhibited by typical numerical examples.

Keywords

Coupled inertial neural networks Synchronization Impulsive control Pinning control Hybrid couplings 

Notes

Acknowledgements

Tianhu Yu was supported by National Natural Science Foundation of China (No. 11902137) and China Postdoctoral Science Foundation (No. 2019M651633); Huamin Wang was supported by National Nature Science Foundation of China(Grant Nos. 61503175, U1804158) and Science and Technology Department Program of Henan Province (Grant No. 172102210407); Jinde Cao was supported by Key Project of Natural Science Foundation of China (No. 61833005); Yang Yang is supported by National Natural Science Foundation of China (No. 11702228).

References

  1. 1.
    Yu T, Cao D, Liu S, Chen H (2016) Stability analysis of neural networks with periodic coefficients and piecewise constant arguments. J Frankl Inst 353:409–425MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Wen S, Zeng Z, Chen MZQ, Huang T (2017) Synchronization of switched neural networks with communication delays via the event-triggered control. IEEE Trans Neural Netw Learn Syst 28(10):2334–2343MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cao J, Manivannan R, Chong KT, Lv X (2019) Enhanced L2–L\(\infty \) state estimation design for delayed neural networks including leakage term via quadratic-type generalized free-matrix-based integral inequality. J Frank Inst 356(13):7371–7392zbMATHCrossRefGoogle Scholar
  4. 4.
    Hu C, Yu J, Chen Z, Jiang H, Huang T (2017) Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks. Neural Netw 89:74–83CrossRefGoogle Scholar
  5. 5.
    Pershin YV, Ventra MD (2010) Experimental demonstration of associative memory with memristive neural networks. Neural Netw 23:881–886CrossRefGoogle Scholar
  6. 6.
    Qi J, Li C, Huang T (2014) Stability of delayed memristive neural networks with time-varying impulses. Cogn Neurodyn 8(5):429–436CrossRefGoogle Scholar
  7. 7.
    Jiang F, Shen Y (2013) Stability of stochastic \(\theta \)-methods for stochastic delay Hopfield neural networks under regime switching. Neural Process Lett 38(3):433–444CrossRefGoogle Scholar
  8. 8.
    Ali MS, Saravanakumar R, Ahn CK, Karimi HR (2017) Stochastic \(H_{\infty }\) filtering for neural networks with leakage delay and mixed time-varying delays. Inf Sci 388–399:118–134Google Scholar
  9. 9.
    Cao Y, Samidurai R, Sriraman R (2019) Stability and dissipativity analysis for neutral type stochastic Markovian jump static neural networks with time delays. J Artif Intell Soft Comput Res 9(3):189–204CrossRefGoogle Scholar
  10. 10.
    Babcock KL, Westervelt RM (1987) Dynamics of simple electronic neural networks. Physica D 28(3):464–469MathSciNetCrossRefGoogle Scholar
  11. 11.
    Yu T, Wang H, Su M, Cao D (2018) Distributed-delay-dependent exponential stability of impulsive neural networks with inertial term. Neurocomputing 313:220–228CrossRefGoogle Scholar
  12. 12.
    Wang L, Zeng Z, Ge MF, Hu J (2018) Global stabilization analysis of inertial memristive recurrent neural networks with discrete and distributed delays. Neural Netw 105:65–74CrossRefGoogle Scholar
  13. 13.
    Maharajan C, Raja R, Cao J, Rajchakit G (2018) Novel global robust exponential stability criterion for uncertain inertial-type BAM neural networks with discrete and distributed time-varying delays via Lagrange sense. J Frankl Inst 355:4727–4754MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Zhang W, Huang T, Li C, Yang J (2018) Robust stability of inertial BAM neural networks with time delays and uncertainties via impulsive effect. Neural Process Lett 48(1):245–256CrossRefGoogle Scholar
  15. 15.
    Huang C, Zhang H, Cao J, Hu H (2019) Stability and Hopf bifurcation of a delayed prey-predator model with disease in the predator. Int J Bifurc Chaos 29(7):1950091MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Zhang G, Zeng Z, Hu J (2018) New results on global exponential dissipativity analysis of memristive inertial neural networks with distributed time-varying delays. Neural Netw 97:183–191CrossRefGoogle Scholar
  17. 17.
    Tu Z, Cao J, Alsaedi A, Alsaadi F (2017) Global dissipativity of memristor-based neutral type inertial neural networks. Neural Netw 88:125–133CrossRefGoogle Scholar
  18. 18.
    Li H, Li C, Zhang W, Jiang X (2018) Global dissipativity of inertial neural networks with proportional delay via new generalized Halanay inequalities. Neural Process Lett 48(3):1543–1561CrossRefGoogle Scholar
  19. 19.
    Yang D, Li X, Qiu J (2019) Output tracking control of delayed switched systems via state-dependent switching and dynamic output feedback. Nonlinear Anal Hybrid Syst 32:294–305MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Gong S, Yang S, Guo Z, Huang T (2018) Global exponential synchronization of inertial memristive neural networks with time-varying delay via nonlinear controller. Neural Netw 102:138–148CrossRefGoogle Scholar
  21. 21.
    Prakash M, Balasubramaniam P, Lakshmanan S (2016) Synchronization of Markovian jumping inertial neural networks and its applications in image encryption. Neural Netw 83:86–93CrossRefGoogle Scholar
  22. 22.
    Rakkiyappan R, Kumari EU, Chandrasekar A, Krishnasamy R (2016) Synchronization and periodicity of coupled inertial memristive neural networks with supremums. Neurocomputing 214:739–749CrossRefGoogle Scholar
  23. 23.
    Rakkiyappan R, Premalatha S, Chandrasekar A, Cao J (2016) Stability and synchronization analysis of inertial memristive neural networks with time delays. Cogn Neurodyn 10(5):437–451CrossRefGoogle Scholar
  24. 24.
    Zhang Y, Liu Y (2020) Nonlinear second-order multi-agent systems subject to antagonistic interactions without velocity constraints. Appl Math Comput 364:124667MathSciNetGoogle Scholar
  25. 25.
    Li B, Lu J, Zhong J, Liu Y (2018) Fast-time stability of temporal Boolean networks. IEEE Trans Neural Netw Learn Syst 30(8):2285–2294MathSciNetCrossRefGoogle Scholar
  26. 26.
    Zhang W, Zuo Z, Wang Y, Zhang Z (2019) Double-integrator dynamics for multiagent systems with antagonistic reciprocity. IEEE Trans Cybern.  https://doi.org/10.1109/TCYB.2019.2939487 CrossRefGoogle Scholar
  27. 27.
    Zhong J, Liu Y, Kou KI, Sun L, Cao J (2019) On the ensemble controllability of Boolean control networks using STP method. Appl Math Comput 358:51–62MathSciNetzbMATHGoogle Scholar
  28. 28.
    Yang X, Li X, Lu J, Cheng Z (2019) Synchronization of time-delayed complex networks with switching topology via hybrid actuator fault and impulsive effects control. IEEE Trans Cybern.  https://doi.org/10.1109/TCYB.2019.2938217 CrossRefGoogle Scholar
  29. 29.
    Zhang L, Yang X, Xu C, Feng J (2017) Exponential synchronization of complex-valued complex networks with time-varying delays and stochastic perturbations via time-delayed impulsive control. Appl Math Comput 306:22–30MathSciNetzbMATHGoogle Scholar
  30. 30.
    Yang X, Lu J, Ho DWC, Song Q (2018) Synchronization of uncertain hybrid switching and impulsive complex networks. Appl Math Model 59:379–392MathSciNetCrossRefGoogle Scholar
  31. 31.
    Yang J, Lu J, Lou J, Liu Y (2020) Synchronization of drive-response Boolean control networks with impulsive disturbances. Appl Math Comput 364:124679MathSciNetCrossRefGoogle Scholar
  32. 32.
    Lakshmanan S, Prakash M, Lim CP, Rakkiyappan R, Balasubramaniam P, Nahavandi S (2016) Synchronization of an inertial neural network with time-varying delays and its application to secure communication. IEEE Trans Neural Netw Learn Syst 29(1):195–207MathSciNetCrossRefGoogle Scholar
  33. 33.
    Wei R, Cao J, Alsaedi A (2018) Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays. Cogn Neurodyn 12(1):121–134CrossRefGoogle Scholar
  34. 34.
    Huang D, Jiang M, Jian J (2017) Finite-time synchronization of inertial memristive neural networks with time-varying delays via sampled-date control. Neurocomputing 266:527–539CrossRefGoogle Scholar
  35. 35.
    Wang Y, Lu J, Liang J, Cao J, Perc M (2018) Pinning synchronization of nonlinear coupled Lure networks under hybrid impulses. IEEE Trans Circuits Syst II Exp Briefs 66(3):432–436CrossRefGoogle Scholar
  36. 36.
    Li B, Lu J, Liu Y, Wu ZG (2019) The outputs robustness of Boolean control networks via pinning control. IEEE Trans Control Netw Syst.  https://doi.org/10.1109/TCNS.2019.2913543 CrossRefGoogle Scholar
  37. 37.
    Liu Y, Li B, Lu J, Cao J (2017) Pinning control for the disturbance decoupling problem of Boolean networks. IEEE Trans Autom Control 62(12):6595–6601MathSciNetzbMATHCrossRefGoogle Scholar
  38. 38.
    Li Y, Lou J, Wang Z, Alsaadi FE (2018) Synchronization of dynamical networks with nonlinearly coupling function under hybrid pinning impulsive controllers. J Frankl Inst 355(14):6520–6530MathSciNetzbMATHCrossRefGoogle Scholar
  39. 39.
    He W, Qian F, Cao J (2017) Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control. Neural Netw 85:1–9zbMATHCrossRefGoogle Scholar
  40. 40.
    Lu J, Ho DWC, Cao J (2010) A unified synchronization criterion for impulsive dynamical networks. Automatica 46:1215–1221MathSciNetzbMATHCrossRefGoogle Scholar
  41. 41.
    Yi C, Feng J, Wang J, Xu C, Zhao Y (2017) Synchronization of delayed neural networks with hybrid coupling via partial mixed pinning impulsive control. Appl Math Comput 312:78–90MathSciNetzbMATHGoogle Scholar
  42. 42.
    Yang X, Lu J (2016) Finite-time Synchronization of coupled networks with Markovian topology and impulsive effects. IEEE Trans Autom Control 61(8):2256–2261MathSciNetzbMATHCrossRefGoogle Scholar
  43. 43.
    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 46:271–291CrossRefGoogle Scholar
  44. 44.
    Yang X, Lam J, Ho DWC, Feng Z (2017) Fixed-time synchronization of complex networks with impulsive effects via non-chattering control. IEEE Trans Autom Control 62(11):5511–5521zbMATHCrossRefGoogle Scholar
  45. 45.
    Yang X, Cao J, Xu C, Feng J (2018) Finite-time stabilization of switched dynamical networks with quantized couplings via quantized controller. Sci China Technol Sci 61(2):299–308CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.School of MathematicsSoutheast UniversityNanjingPeople’s Republic of China
  2. 2.Department of MathematicsLuoyang Normal UniversityLuoyangPeople’s Republic of China
  3. 3.School of Mechanical EngineeringSouthwest Jiaotong UniversityChengduPeople’s Republic of China

Personalised recommendations