IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i24p4828-d1007855.html
   My bibliography  Save this article

Zeroing Neural Networks Combined with Gradient for Solving Time-Varying Linear Matrix Equations in Finite Time with Noise Resistance

Author

Listed:
  • Jun Cai

    (School of Cyber Security, Guangdong Polytechnic Normal University, Guangzhou 510635, China)

  • Wenlong Dai

    (School of Cyber Security, Guangdong Polytechnic Normal University, Guangzhou 510635, China)

  • Jingjing Chen

    (School of Cyber Security, Guangdong Polytechnic Normal University, Guangzhou 510635, China)

  • Chenfu Yi

    (School of Cyber Security, Guangdong Polytechnic Normal University, Guangzhou 510635, China)

Abstract

Due to the time delay and some unavoidable noise factors, obtaining a real-time solution of dynamic time-varying linear matrix equation (LME) problems is of great importance in the scientific and engineering fields. In this paper, based on the philosophy of zeroing neural networks (ZNN), we propose an integration-enhanced combined accelerating zeroing neural network (IEAZNN) model to solve LME problem accurately and efficiently. Different from most of the existing ZNNs research, there are two error functions combined in the IEAZNN model, among which the gradient of the energy function is the first design for the purpose of decreasing the norm-based error to zero and the second one is adding an integral term to resist additive noise. On the strength of novel combination in two error functions, the IEAZNN model is capable of converging in finite time and resisting noise at the same time. Moreover, theoretical proof and numerical verification results show that the IEAZNN model can achieve high accuracy and fast convergence speed in solving time-varying LME problems compared with the conventional ZNN (CZNN) and integration-enhanced ZNN (IEZNN) models, even in various kinds of noise environments.

Suggested Citation

  • Jun Cai & Wenlong Dai & Jingjing Chen & Chenfu Yi, 2022. "Zeroing Neural Networks Combined with Gradient for Solving Time-Varying Linear Matrix Equations in Finite Time with Noise Resistance," Mathematics, MDPI, vol. 10(24), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4828-:d:1007855
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/24/4828/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/24/4828/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zhiguo Tan, 2022. "Fixed-Time Convergent Gradient Neural Network for Solving Online Sylvester Equation," Mathematics, MDPI, vol. 10(17), pages 1-13, August.
    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.

      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:gam:jmathe:v:10:y:2022:i:24:p:4828-:d:1007855. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      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.