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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
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    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. Zhang, Xin-Fang & Wang, Qing-Wen, 2021. "Developing iterative algorithms to solve Sylvester tensor equations," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    4. 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).
    5. 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).
    6. 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).
    7. 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).
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