Skip to main content

Advertisement

SpringerLink
Log in

LMIs conditions to robust pinning synchronization of uncertain fractional-order neural networks with discontinuous activations

  • Foundations
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

This paper deals with the robust pinning synchronization issue of uncertain fractional-order neural networks with discontinuous activations (FNNDAs) by means of the linear matrix inequalities (LMIs). In this paper, a class of FNNDAs model is presented. Moreover, an appropriate pinning controller is designed to ensure the error dynamical system gets robust Mittag–Leffler stability via Lyapunov function approach, non-smooth analysis theory and inequality analysis technique. In addition, the robust pinning synchronization conditions of FNNDAs drive system and FNNDAs response system are obtained in terms of the LMIs. Finally, a typical numerical simulation is provided to show the effectiveness of the obtained results.

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
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Anbalagan P, Ramachandran R, Cao J et al (2019) Global robust synchronization of fractional order complex valued neural networks with mixed time varying delays and impulses. Int J Control Autom Syst 17(2):509–520

    Article  Google Scholar 

  • Boyd B, Ghoui LE, Feron E et al (1998) Linear matrix inequalities in system and control theory. Proc IEEE 86(12):2473–2474

    Article  Google Scholar 

  • Chen L, Chai Y, Wu R (2011) Linear matrix inequality criteria for robust synchronization of uncertain fractional-order chaotic systems. Chaos 21:043107

    Article  MathSciNet  Google Scholar 

  • Chen L, Chai Y, Wu R, Yang J (2012) Stability and stabilization of a class of nonlinear fractional-order systems with Caputo derivative. IEEE Trans Circuits Syst II Express Briefs 59(9):602–606

    Article  Google Scholar 

  • Ding Z, Shen Y (2016) Projective synchronization of nonidentical fractional-order neural networks based on sliding mode controller. Neural Netw 76:97–105

    Article  Google Scholar 

  • Ding Z, Shen Y, Wang L (2016) Global Mittag–Leffler synchronization of fractional-order neural networks with discontinuous activations. Neural Netw 73:77–85

    Article  Google Scholar 

  • Forti M, Nistri P (2003) Global convergence of neural networks with discontinuous neuron activations. IEEE Trans Circuits Syst I Fundam Theory Appl 50(11):1421–1435

    Article  MathSciNet  Google Scholar 

  • Forti M, Nistri P, Papini D (2005) Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain. IEEE Trans Neural Netw 16(6):1449–1463

    Article  Google Scholar 

  • Hilfer R (2000) Applications of fractional calculus in physics. World Scientific, Hackensack

    Book  Google Scholar 

  • Jiang X, Xu M (2010) The time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems. Physica A 389(17):3368–3374

    Article  MathSciNet  Google Scholar 

  • Kilbas AA, Srivastava HM, Trujillo JJ et al (2006) Theory and application of fractional differential equations (North-Holland Mathematics Studies), vol 204. Elsevier Science Inc, New York

    Google Scholar 

  • Zhang H, Liu B, Shao K et al (2018) Linear matrix inequality criteria for robust synchronization of singular fractional-order complex dynamical networks. J Jili Univ (Inf Sci edn) 36(1):26–33

    Google Scholar 

  • Koeller RC (1984) Application of fractional calculus to the theory of viscoelasticity. J Appl Mech 51(2):299–307

    Article  MathSciNet  Google Scholar 

  • Liu DY, Zheng G, Boutat D, Liu HR (2012) Non-asymptotic fractional order differentiator for a class of fractional order linear systems. Automatica 78:61–71

    Article  MathSciNet  Google Scholar 

  • Liu H, Pan Y, Li S et al (2018) Synchronization for fractional-order neural networks with full/under-actuation using fractional-order sliding mode control. Int J Mach Learn Cybernet 9(7):1219–1232

    Article  Google Scholar 

  • Liu S, Yu Y, Zhang S (2019) Robust synchronization of memristor-based fractional-order Hopfield neural networks with parameter uncertainties. Neural Comput Appl 31:3533–3542

    Article  Google Scholar 

  • Liu H, Pan Y, Cao J et al (2020) Positivity and stability analysis for fractional-order delayed systems: a T–S fuzzy model approach. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2020.2966420

    Article  Google Scholar 

  • Peng X, Wu H (2018) Robust Mittag–Leffler synchronization for uncertain fractional-order discontinuous neural networks via non-fragile control strategy. Neural Process Lett 48(3):1521–1542

    Article  Google Scholar 

  • Ren J, Wu H (2018) Global synchronization in the finite Time for variable-order fractional neural networks with discontinuous activations. Opt Mem Neural Netw 27(2):100–112

    Article  Google Scholar 

  • Stamova I, Stamov G (2017) Mittag–Leffler synchronization of fractional neural networks with time-varying delays and reaction–diffusion terms using impulsive and linear controllers. Neural Netw 96:22–32

    Article  Google Scholar 

  • Velmurugan G, Rakkiyappan R (2016) Finite-time synchronization of fractional-order memristor-based neural networks with time delays. Nonlinear Dyn 73:36–46

    MATH  Google Scholar 

  • Wang S, Huang Y, Ren S (2017) Synchronization and robust synchronization for fractional-order coupled neural networks. IEEE Access 5:12439–12448

    Article  Google Scholar 

  • Wei X, Liu DY, Boutat D (2016) Non-asymptotic pseudo-state estimation for a class of fractional order linear systems. IEEE Trans Autom Control 62(3):1150–1164

    Article  Google Scholar 

  • Wu H, Zhang X, Xue S et al (2016) LMI conditions to global Mittag–Leffler stability of fractional-order neural networks with impulses. Neurocomputing 193:148–154

    Article  Google Scholar 

  • Wu H, Wang L, Niu P et al (2017) Global projective synchronization in finite time of nonidentical fractional-order neural networks based on sliding mode control strategy. Neurocomputing 235:264–273

    Article  Google Scholar 

  • Yi C, Feng J, Wang J et al (2018) Pinning synchronization of nonlinear and delayed coupled neural networks with multi-weights via aperiodically intermittent control. Neural Process Lett 49(1):141–157

    Article  Google Scholar 

  • 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(1):239–262

    Article  Google Scholar 

  • Zhang L, Yang Y, Wang F (2017) Synchronization analysis of fractional-order neural networks with time-varying delays via discontinuous neuron activations. Neurocomputing 275:40–49

    Article  Google Scholar 

Download references

Acknowledgements

The authors are extremely grateful to Editors and Reviewers for their careful reading of the manuscript and insightful comments, which help to enrich the content of the paper and improve the presentation of the results in the paper. This work was funded by the Program for the Top Young Talents of Higher Learning Institutions of Hebei (BJ2017033) and the Natural Science Foundation of Hebei Province of China (A2018203288).

Author information

Authors and Affiliations

  1. School of Information Engineering, Tianjin University of Commerce, Tianjin, China

    Xinxin Zhang & Yunpeng Ma

Authors
  1. Xinxin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yunpeng Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yunpeng Ma.

Ethics declarations

Conflict of interest

All authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Communicated by A. Di Nola.

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

Zhang, X., Ma, Y. LMIs conditions to robust pinning synchronization of uncertain fractional-order neural networks with discontinuous activations. Soft Comput 24, 15927–15935 (2020). https://doi.org/10.1007/s00500-020-05315-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-020-05315-7

Keywords

Search

Navigation