IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v452y2023ics0096300323002412.html
   My bibliography  Save this article

Finite-time zeroing neural networks with novel activation function and variable parameter for solving time-varying Lyapunov tensor equation

Author

Listed:
  • Qi, Zhaohui
  • Ning, Yingqiang
  • Xiao, Lin
  • Luo, Jiajie
  • Li, Xiaopeng

Abstract

Time-varying Lyapunov tensor equation (TV-LTE) is an extension of time-varying Lyapunov matrix equation (TV-LME), which represents more dimensions of data. In order to solve the TV-LTE more effectively, this paper proposes two improved zeroing neural network (ZNN) models based on a novel activation function and variable parameter, which have shorter convergence time and computation time. The novel activation function is composed of an exponential function and a sign-bi-power (SBP) function, which is mentioned as the exponential SBP (ESBP) function. Then, based on the ESBP activation function and the standard ZNN design method, an ESBP zeroing neural network (ES-ZNN) model is first provided. In addition, considering the relationship among the error matrix, design parameter and computational efficiency, this paper further designs an exponential parameter that varies dynamically with time and the error matrix. Replacing the fixed parameter with the proposed exponential variable parameter, an exponentially variable parameter ES-ZNN (EVPES-ZNN) model is provided to enhance the computational efficiency and convergence performance of the ES-ZNN model. Furthermore, the upper bounds on convergence time of such two ZNN models are theoretically calculated. Simulation experiments demonstrate the theoretical conclusion that the ES-ZNN and EVPES-ZNN models are able to solve the TV-LTE in finite-time.

Suggested Citation

  • Qi, Zhaohui & Ning, Yingqiang & Xiao, Lin & Luo, Jiajie & Li, Xiaopeng, 2023. "Finite-time zeroing neural networks with novel activation function and variable parameter for solving time-varying Lyapunov tensor equation," Applied Mathematics and Computation, Elsevier, vol. 452(C).
    • Handle: RePEc:eee:apmaco:v:452:y:2023:i:c:s0096300323002412
    DOI: 10.1016/j.amc.2023.128072
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300323002412
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2023.128072?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Xiao, Lin & Li, Xiaopeng & Jia, Lei & Liu, Sai, 2022. "Improved finite-time solutions to time-varying Sylvester tensor equation via zeroing neural networks," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    2. Guo, Dongsheng & Zhang, Yunong, 2015. "ZNN for solving online time-varying linear matrix–vector inequality via equality conversion," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 327-338.
    3. Kaltenbacher, Stefan & Steinberger, Martin & Horn, Martin, 2022. "Pipe roughness identification of water distribution networks: A Tensor method," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    4. Huang, Baohua & Ma, Changfeng, 2020. "Global least squares methods based on tensor form to solve a class of generalized Sylvester tensor equations," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    5. Zhang, Xin-Fang & Wang, Qing-Wen, 2021. "Developing iterative algorithms to solve Sylvester tensor equations," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    6. Weijermars, Ruud & Pham, Tri & Ettehad, Mahmood, 2020. "Linear superposition method (LSM) for solving stress tensor fields and displacement vector fields: Application to multiple pressure-loaded circular holes in an elastic plate with far-field stress," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    7. Khosravi Dehdezi, Eisa & Karimi, Saeed, 2022. "A rapid and powerful iterative method for computing inverses of sparse tensors with applications," Applied Mathematics and Computation, Elsevier, vol. 415(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xiao, Lin & Li, Xiaopeng & Jia, Lei & Liu, Sai, 2022. "Improved finite-time solutions to time-varying Sylvester tensor equation via zeroing neural networks," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    2. Huang, Guang-Xin & Chen, Qi-Xing & Yin, Feng, 2022. "Preconditioned TBiCOR and TCORS algorithms for solving the Sylvester tensor equation," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    3. Eisa Khosravi Dehdezi, 2021. "Iterative Methods for Solving Sylvester Transpose Tensor Equation $$~\mathcal A\star _N\mathcal X\star _M\mathcal {B}+\mathcal {C}\star _M\mathcal X^T\star _N\mathcal {D}=\mathcal {E}$$ A ⋆ N X ⋆ M B ," SN Operations Research Forum, Springer, vol. 2(4), pages 1-21, December.
    4. Bolin Liao & Cheng Hua & Xinwei Cao & Vasilios N. Katsikis & Shuai Li, 2022. "Complex Noise-Resistant Zeroing Neural Network for Computing Complex Time-Dependent Lyapunov Equation," Mathematics, MDPI, vol. 10(15), pages 1-17, August.
    5. Zhu, Jingcan & Jin, Jie & Chen, Weijie & Gong, Jianqiang, 2022. "A combined power activation function based convergent factor-variable ZNN model for solving dynamic matrix inversion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 291-307.
    6. Ruud Weijermars & Jihoon Wang, 2021. "Stress Reversals near Hydraulically Fractured Wells Explained with Linear Superposition Method (LSM)," Energies, MDPI, vol. 14(11), pages 1-22, June.
    7. Chen, Qi-Xing & Huang, Guang-Xin & Zhang, Ming-Yue, 2024. "Preconditioned BiCGSTAB and BiCRSTAB methods for solving the Sylvester tensor equation," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    8. Tri Pham & Ruud Weijermars, 2020. "Hydraulic Fracture Propagation in a Poro-Elastic Medium with Time-Dependent Injection Schedule Using the Time-Stepped Linear Superposition Method (TLSM)," Energies, MDPI, vol. 13(24), pages 1-22, December.
    9. Zhang, Xin-Fang & Wang, Qing-Wen, 2021. "Developing iterative algorithms to solve Sylvester tensor equations," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    10. Khosravi Dehdezi, Eisa & Karimi, Saeed, 2022. "A rapid and powerful iterative method for computing inverses of sparse tensors with applications," Applied Mathematics and Computation, Elsevier, vol. 415(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:452:y:2023:i:c:s0096300323002412. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.