Skip to main content

Advertisement

SpringerLink
Log in

Asymptotic stability of singular delayed reaction-diffusion neural networks

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

The asymptotic stability of delayed reaction-diffusion neural networks with algebraic constraints, that is, singular delayed reaction-diffusion neural networks, is studied in this paper. In terms of Green’s theorem, inequality technique and linear matrix inequalities (LMIs), two less conservative criterion for the asymptotic stability of singular delayed reaction-diffusion neural networks are given by endowing Lyapunov direct method and used to design an appropriate stabilizing feedback controllers. The results address both the effects of the delay and the algebraic constraints. In addition, these conditions have higher computational efficiency and can easily detect and stabilize the actual neural networks. Finally, the numerical simulations verify the validity 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

Similar content being viewed by others

References

  1. Le W, Xu Z, Kun W, Xiang C, Xun C (2020) Improved high-density myoelectric pattern recognition control against electrode shift using data augmentation and dilated convolutional neural network. IEEE Trans Neural Syst Rehabilit Eng. https://doi.org/10.1109/TNSRE.2020.3030931

    Article  Google Scholar 

  2. Efe MO, Kaynak O (2000) Stabilizing and robustifying the learning mechanisms of artificial neural networks in control engineering applications. Int J Intell Syst 15:365–388

    Article  Google Scholar 

  3. Aouiti C, Assali E (2019) Nonlinear Lipschitz measure and adaptive control for stability and synchronization in delayed inertial Cohen-Grossberg-type neural networks. Int J Adapt Control Signal Process 33:1457–1477

    Article  MathSciNet  Google Scholar 

  4. Aouiti C, Assali E (2019) Stability analysis for a class of impulsive high-order Hopfield neural networks with leakage time-varying delays. Neural Comput Appl 31:7781–7803

    Article  Google Scholar 

  5. Aouiti C, Assali E (2019) Stability analysis for a class of impulsive bidirectional associative memory (BAM) neural networks with distributed delays and leakage time-varying delays. Neural Process Lett 50:851–885

    Article  Google Scholar 

  6. Sedighi R, Meiabadi M, Sedighi M (2017) Optimisation of gate location based on weld line in plastic injection moulding using computeraided engineering, artificial neural network, and genetic algorithm, International Journal of Automotive and Mechanical. Engineering 14:4419–4431

    Google Scholar 

  7. Ahmed I, Iqbal MJ, Basheri M (2020) Biological data classification and analysis using convolutional neural network. J Med Imaging Health Inf 10:2459–2465

    Article  Google Scholar 

  8. Gunther J, Reichensdorfer E, Pilarski PM, Diepold K (2020) Interpretable PID parameter tuning for control engineering using general dynamic neural networks: An extensive comparison, PLoS ONE, 15, Article ID: e0243320

  9. Fernandez-Blanco E, Rivero D, Pazos A (2020) EEG signal processing with separable convolutional neural network for automatic scoring of sleeping stage. Neurocomputing 410:220–228

    Article  Google Scholar 

  10. Spoerer CJ, Kietzmann TC, Mehrer J, Charest I, Kriegeskorte N (2020) Recurrent neural networks can explain flexible trading of speed and accuracy in biological vision, PLoS Comput Biol, 16, Article ID: e1008215

  11. Liu XZ, Li ZT, Wu KN (2020) Boundary Mittag-Leffler stabilization of fractional reaction-diffusion cellular neural networks. Neural Netw 132:269–280

    Article  Google Scholar 

  12. Liu XZ, Wu KN, Zhang WH (2020) Intermittent boundary stabilization of stochastic reaction-diffusion Cohen-Grossberg neural networks. Neural Netw 131:1–13

    Article  Google Scholar 

  13. Wang LM, He HB, Zeng ZG, Hu C (2020) Global stabilization of fuzzy memristor-based reaction-diffusion neural networks. IEEE Trans Cybern 50:4658–4669

    Article  Google Scholar 

  14. Aouiti C, Jallouli H (2021) State feedback controllers based finite-time and fixed-time stabilisation of high order BAM with reaction-diffusion term. Int J Syst Sci 52:905–927

    Article  MathSciNet  Google Scholar 

  15. Wu T, Cao JD, Xiong LL, Xie XQ (2020) New results on stability analysis and extended dissipative conditions for uncertain memristive neural networks with two additive time-varying delay components and reaction-diffusion terms. Int J Robust Nonlinear Control 30:6535–6568

    Article  MathSciNet  Google Scholar 

  16. Sheng Y, Zhang H, Zeng ZG (2020) Stability and robust stability of stochastic reaction-diffusion neural networks with infinite discrete and distributed delays. IEEE Trans Syst Man Cybern Syst 50:1721–1732

    Article  Google Scholar 

  17. Wei TD, Lin P, Wang YF, Wang LS (2019) Stability of stochastic impulsive reaction-diffusion neural networks with S-type distributed delays and its application to image encryption. Neural Netw 116:35–45

    Article  Google Scholar 

  18. Hou J, Huang YL, Yang EF (2019) \(\Psi\)-type stability of reaction-diffusion neural networks with time-varying discrete delays and bounded distributed delays. Neurocomputing 340:281–293

    Article  Google Scholar 

  19. Lv TS, Gan QT, Xiao F (2019) Stability for a class of generalized reaction-diffusion uncertain stochastic neural networks with mixed delays. Int J Mach Learn Cybern 10:967–978

    Article  Google Scholar 

  20. Rao RF, Zhong SM, Pu ZL (2019) Fixed point and p-stability of T-S fuzzy impulsive reaction-diffusion dynamic neural networks with distributed delay via Laplacian semigroup. Neurocomputing 335:170–184

    Article  Google Scholar 

  21. Yang ZC, Zhou WS, Huang TW (2019) Input-to-state stability of delayed reaction-diffusion neural networks with impulsive effects. Neurocomputing 333:261–272

    Article  Google Scholar 

  22. Edwards D (2002) Process safety and environmental protection - Editorial - SH&E performance - Objective(s) or constraints? Process Saf Environ Prot 80:287–288

    Article  Google Scholar 

  23. Ferris JM (2015) Procurement costs and tool performance requirements: determining constraints on lithic toolstone selection in baja california sur

  24. Studli S, Corless M, Middleton RH, Shorten R (2017) On the AIMD algorithm under saturation constraints. IEEE Trans Autom Control 62:6392–6398

    Article  MathSciNet  Google Scholar 

  25. Martinez CA, Wang CJ (2015) Structural constraints on learning in the neural network. J Neurophysiol 114:2555–2557

    Article  Google Scholar 

  26. Maggini M, Melacci S, Sarti L (2012) Learning from pairwise constraints by similarity neural networks. Neural Netw 26:141–158

    Article  Google Scholar 

  27. Xiong WJ, Yu XH, Patel R, Huang TW (2018) Stability of singular discrete-time neural networks with state-dependent coefficients and run-to-run control strategies. IEEE Trans Neural Netw Learn Syst 12:6415–6420

    Article  MathSciNet  Google Scholar 

  28. Zhang YQ, Shi P, Agarwal RK, Shi Y (2020) Event-based dissipative analysis for discrete time-delay singular jump neural networks. IEEE Trans Neural Netw Learn Syst 31:1232–1241

    Article  MathSciNet  Google Scholar 

  29. Ma YC, Ma NN, Chen L, Zheng YQ, Han Y (2019) Exponential stability for the neutral-type singular neural network with time-varying delays. Int J Mach Learn Cybern 10:853–858

    Article  Google Scholar 

  30. Liu S, Zhou XF, Li X, Jiang W (2016) Stability of fractional nonlinear singular systems and its applications in synchronization of complex dynamical networks. Nonlinear Dyn 84:2377–2385

    Article  MathSciNet  Google Scholar 

  31. Liu S, Li X, Zhou XF, Jiang W (2015) Synchronization analysis of singular dynamical networks with unbounded time-delays. Adv Differ Equ 193:1–9

    MathSciNet  MATH  Google Scholar 

  32. Wu H, Zhang X, Li R, Yao R (2015) Synchronization of reaction-diffusion neural networks with mixed time-varying delays. J Control Autom Electrical Syst 26:16–27

    Article  Google Scholar 

  33. Chen LP, Huang TW, Machado JA, Lopes AM, Chai Y, Wu RC (2019) Delay-dependent criterion for asymptotic stability of a class of fractional-order memristive neural networks with time-varying delays. Neural Netw 118:289–299

    Article  Google Scholar 

  34. Ma YC, Zheng YQ (2018) Delay-dependent stochastic stability for discrete singular neural networks with Markovian jump and mixed time-delays. Neural Comput Appl 29:111–122

    Article  Google Scholar 

  35. Zhang H, Sheng Y, Zeng Z (2018) Synchronization of coupled reaction-diffusion neural networks with directed topology via an adaptive approach. IEEE Trans Neural Netw Learn Syst 29:1550–1561

    Article  MathSciNet  Google Scholar 

  36. Lu GP, Ho DWC (2006) Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation. IEEE Trans Autom Control 51:818–823

    Article  MathSciNet  Google Scholar 

  37. Gilbarg D, Trudinger NS (1991) Elliptic partial differential equations of second order. Springer, Berklin

    MATH  Google Scholar 

  38. Li RX, Cao JD (2016) Stability analysis of reaction-diffusion uncertain memristive neural networks with time-varying delays and leakage term. Appl Math Comput 278:54–69

    MathSciNet  MATH  Google Scholar 

  39. Zhang RM, Zeng DQ, Park JH, Liu YJ, Xie XP (2020) Adaptive event-triggered synchronization of reaction-diffusion neural networks. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.3027284

    Article  Google Scholar 

  40. Song XN, Man JT, Song S, Ahn CK (2020) Gain-scheduled finite-time synchronization for reaction-diffusion memristive neural networks subject to inconsistent markov chains. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.3009081

    Article  Google Scholar 

  41. Liu PC, Cao GY (2020) Employing the Friedrichs inequality to ensure global exponential stability of delayed reaction-diffusion neural networks with nonlinear boundary conditions. Neurocomputing 383:81–94

    Article  Google Scholar 

Download references

Acknowledgements

This research is supported by the National Natural Science Foundation of China (Nos. U1806203 and 61533011).

Author information

Authors and Affiliations

  1. School of Control Science and Technology, Shandong University, Jinan, 250061, People’s Republic of China

    Xiang Wu, Shutang Liu & Zhimin Bi

  2. Institute of Marine Science and Technology, Shandong University, Qingdao, 266237, People’s Republic of China

    Yin Wang

Authors
  1. Xiang Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shutang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhimin Bi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shutang Liu.

Ethics declarations

Conflict of Interest

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be constructed as influencing the position presented in, or the review of, the manuscript entitled.

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

Wu, X., Liu, S., Wang, Y. et al. Asymptotic stability of singular delayed reaction-diffusion neural networks. Neural Comput & Applic 34, 8587–8595 (2022). https://doi.org/10.1007/s00521-021-06740-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-021-06740-x

Keywords

Search

Navigation