IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v178y2024ics0960077923011876.html
   My bibliography  Save this article

A flexible-predefined-time convergence and noise-suppression ZNN for solving time-variant Sylvester equation and its application to robotic arm

Author

Listed:
  • Zheng, Boyu
  • Han, Zhiyong
  • Li, Chunquan
  • Zhang, Zhijun
  • Yu, Junzhi
  • Liu, Peter X.

Abstract

Although the zeroing neural network (ZNN) has strong competitiveness in solving the time-varying Sylvester equation (TVSE), its convergence and robustness as two key indicators still need to be further improved. To address these problems, we propose a flexible-predefined-time convergence and noise-suppression ZNN (FPCNS-ZNN). Different from most existing ZNN variants, the proposed FPCNS-ZNN provides the following three new improvements: (1) In FPCNS-ZNN, a new specially designed time-variant-gain (SD-TVG) is proposed to better improve the convergence speed at each stage of iterative computation. (2) In FPCNS-ZNN, a new flexible nonlinear activation function (FN-AF) is proposed to flexibly control the convergence speed and predefine convergence time with certain robustness. (3) SD-TVG and FN-AF are dexterously combined to construct the new FPCNS-ZNN, which can obtain faster convergence speed and stronger robustness. Through detailed theoretical analysis and mathematical derivation, the proposed FPCNS-ZNN model has been confirmed to have promising stability, flexible-predefined-time, and strong robustness. It should be noted that the predefined-time upper bound of the proposed FPCNS-ZNN is accurately calculated by dexterously using the Beta function. Computer simulations and comparative experiments indicate that the proposed FPCNS-ZNN has faster convergence speed and stronger robustness compared with three state-of-the-art ZNN variants. Finally, the proposed FPCNS-ZNN is used to solve the motion planning problem of the robotic arm, and the experiment results illustrate the utility of the model.

Suggested Citation

  • Zheng, Boyu & Han, Zhiyong & Li, Chunquan & Zhang, Zhijun & Yu, Junzhi & Liu, Peter X., 2024. "A flexible-predefined-time convergence and noise-suppression ZNN for solving time-variant Sylvester equation and its application to robotic arm," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:chsofr:v:178:y:2024:i:c:s0960077923011876
    DOI: 10.1016/j.chaos.2023.114285
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923011876
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.114285?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. Wang, Guancheng & Li, Qinrou & Liu, Shaoqing & Xiao, Hua & Zhang, Bob, 2022. "New zeroing neural network with finite-time convergence for dynamic complex-value linear equation and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Xiao, Lin & Li, Linju & Cao, Penglin & He, Yongjun, 2023. "A fixed-time robust controller based on zeroing neural network for generalized projective synchronization of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Jin, Jie & Chen, Weijie & Qiu, Lixin & Zhu, Jingcan & Liu, Haiyan, 2023. "A noise tolerant parameter-variable zeroing neural network and its applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 482-498.
    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. Hang Yi & Wenjun Peng & Xiuchun Xiao & Shaojin Feng & Hengde Zhu & Yudong Zhang, 2023. "An Adaptive Zeroing Neural Network with Non-Convex Activation for Time-Varying Quadratic Minimization," Mathematics, MDPI, vol. 11(11), pages 1-15, June.
    2. Miao, Peng & Zheng, Yuhua & Li, Shuai, 2024. "A new FXTZNN model for solving TVCS equation and application to pseudo-inverse of a matrix," Applied Mathematics and Computation, Elsevier, vol. 465(C).
    3. Fang, Qi & Wang, Mingzhu & Li, Xiaodi, 2023. "Event-triggered distributed delayed impulsive control for nonlinear systems with applications to complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

    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:chsofr:v:178:y:2024:i:c:s0960077923011876. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.