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Zeroing Neural Network With Coefficient Functions and Adjustable Parameters for Solving Time-Variant Sylvester

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    A new Zeroing Neural Network with Coefficient Functions and Adjustable Parameters (ZNN-CFAP) model offers faster solutions for time-variant Sylvester equations. This advanced model demonstrates superior convergence rates and practical applications in robotics.

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    Area of Science:

    • Computational mathematics
    • Neural network theory
    • Control systems engineering

    Background:

    • The time-variant Sylvester equation is a critical problem in control theory and system analysis.
    • Previous methods, such as the Zeroing Neural Network with Sign-Bi-Power Function (ZNN-SBPF), have been used but improvements in convergence speed are sought.
    • Existing Zeroing Neural Network (ZNN) models require enhancements for efficiency in solving complex dynamic equations.

    Purpose of the Study:

    • To propose a novel Zeroing Neural Network with Coefficient Functions and Adjustable Parameters (ZNN-CFAP) model.
    • To enhance the convergence rate for solving time-variant Sylvester equations compared to existing ZNN models.
    • To theoretically prove the finite-time convergence and establish an upper bound for the convergence time of the proposed ZNN-CFAP model.

    Main Methods:

    • Development of the ZNN-CFAP model, incorporating adaptable coefficient functions and adjustable parameters.
    • Theoretical analysis to establish finite-time convergence properties and derive the convergence time upper bound.
    • Implementation of computer simulations and numerical experiments to validate the model's performance.

    Main Results:

    • The ZNN-CFAP model demonstrates significantly improved convergence rates in solving time-variant Sylvester equations.
    • Theoretical proofs confirm the finite-time convergence and provide an upper bound for the convergence time.
    • Comparative experiments show the ZNN-CFAP model outperforms ZNN-SBPF and ZNN-LF in terms of convergence speed.

    Conclusions:

    • The proposed ZNN-CFAP model is an effective and efficient method for solving time-variant Sylvester equations.
    • The model's practical utility is validated through successful application in robot manipulator tracking control.
    • The ZNN-CFAP model represents a significant advancement in neural network approaches for dynamic system equations.