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Fixed-Time Convergent Gradient Neural Network for Solving Online Sylvester Equation

Author

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  • Zhiguo Tan

    (School of Information Engineering, Guangzhou Panyu Polytechnic, Guangzhou 511483, China)

Abstract

This paper aims at finding a fixed-time solution to the Sylvester equation by using a gradient neural network (GNN). To reach this goal, a modified sign-bi-power (msbp) function is presented and applied on a linear GNN as an activation function. Accordingly, a fixed-time convergent GNN (FTC-GNN) model is developed for solving the Sylvester equation. The upper bound of the convergence time of such an FTC-GNN model can be predetermined if parameters are given regardless of the initial conditions. This point is corroborated by a detailed theoretical analysis. In addition, the convergence time is also estimated utilizing the Lyapunov stability theory. Two examples are then simulated to demonstrate the validation of the theoretical analysis, as well as the superior convergence performance of the presented FTC-GNN model as compared to the existing GNN models.

Suggested Citation

  • Zhiguo Tan, 2022. "Fixed-Time Convergent Gradient Neural Network for Solving Online Sylvester Equation," Mathematics, MDPI, vol. 10(17), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3090-:d:899721
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    References listed on IDEAS

    as
    1. Juan Zhang & Xiao Luo, 2022. "Gradient-Based Optimization Algorithm for Solving Sylvester Matrix Equation," Mathematics, MDPI, vol. 10(7), pages 1-14, March.
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    Cited by:

    1. 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.

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