IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i24p4913-d1297276.html
   My bibliography  Save this article

A New Method for Dynamical System Identification by Optimizing the Control Parameters of Legendre Multiwavelet Neural Network

Author

Listed:
  • Xiaoyang Zheng

    (School of Artificial Intelligence, Chongqing University of Technology, Chongqing 400054, China)

  • Shiyu Liu

    (School of Artificial Intelligence, Chongqing University of Technology, Chongqing 400054, China)

  • Zejiang Yu

    (School of Artificial Intelligence, Chongqing University of Technology, Chongqing 400054, China)

  • Chengyou Luo

    (School of Artificial Intelligence, Chongqing University of Technology, Chongqing 400054, China)

Abstract

Wavelet neural networks have been widely applied to dynamical system identification fields. The most difficult issue lies in selecting the optimal control parameters (the wavelet base type and corresponding resolution level) of the network structure. This paper utilizes the advantages of Legendre multiwavelet (LW) bases to construct a Legendre multiwavelet neural network (LWNN), whose simple structure consists of an input layer, hidden layer, and output layer. It is noted that the activation functions in the hidden layer are adopted as LW bases. This selection if based on the its rich properties of LW bases, such as piecewise polynomials, orthogonality, various regularities, and more. These properties contribute to making LWNNs more effective in approximating the complex characteristics exhibited by uncertainties, step, nonlinear, and ramp in the dynamical systems compared to traditional wavelet neural networks. Then, the number of selection LW bases and the corresponding resolution level are effectively optimized by the simple Genetic Algorithm, and the improved gradient descent algorithm is implemented to learn the weight coefficients of LWNN. Finally, four nonlinear dynamical system identification problems are applied to validate the efficiency and feasibility of the proposed LWNN-GA method. The experiment results indicate that the LWNN-GA method achieves better identification accuracy with a simpler network structure than other existing methods.

Suggested Citation

  • Xiaoyang Zheng & Shiyu Liu & Zejiang Yu & Chengyou Luo, 2023. "A New Method for Dynamical System Identification by Optimizing the Control Parameters of Legendre Multiwavelet Neural Network," Mathematics, MDPI, vol. 11(24), pages 1-26, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4913-:d:1297276
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/24/4913/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/24/4913/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Rafiq, Naila & Shoaib, Muhammad & Kiani, Adiqa Kausar & Shu, Chi-Min, 2022. "Design of intelligent computing networks for nonlinear chaotic fractional Rossler system," Chaos, Solitons & Fractals, Elsevier, vol. 157(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. Ren, Lujie & Mou, Jun & Banerjee, Santo & Zhang, Yushu, 2023. "A hyperchaotic map with a new discrete memristor model: Design, dynamical analysis, implementation and application," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Alquhayz, Hani & Abdalla, Manal Z.M. & Alhagyan, Mohammed & Gargouri, Ameni & Shoaib, Muhammad, 2023. "Design of intelligent hybrid NAR-GRNN paradigm for fractional order VDP chaotic system in cardiac pacemaker with relaxation oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    3. Alsaade, Fawaz W. & Yao, Qijia & Bekiros, Stelios & Al-zahrani, Mohammed S. & Alzahrani, Ali S. & Jahanshahi, Hadi, 2022. "Chaotic attitude synchronization and anti-synchronization of master-slave satellites using a robust fixed-time adaptive controller," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    4. Jun-Juh Yan & Hang-Hong Kuo, 2022. "Adaptive Memoryless Sliding Mode Control of Uncertain Rössler Systems with Unknown Time Delays," Mathematics, MDPI, vol. 10(11), pages 1-13, May.

    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:11:y:2023:i:24:p:4913-:d:1297276. 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.