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General Square-Pattern Discretization Formulas via Second-Order Derivative Elimination for Zeroing Neural Network

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    This study introduces general square-pattern discretization (SPD) formulas for zeroing neural networks (ZNN), unifying existing methods. These new formulas enhance ZNN model stability and performance in optimization tasks.

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    Area of Science:

    • Neural Networks
    • Numerical Analysis
    • Robotics

    Background:

    • Existing zeroing neural network (ZNN) discretization formulas have limitations in precision and development methodology.
    • Previous square-pattern discretization (SPD) formulas were often developed through trial and error.

    Purpose of the Study:

    • To propose general square-pattern discretization (SPD) formulas for ZNN.
    • To establish a unified framework encompassing all existing SPD formulas.
    • To investigate the application of these formulas in solving optimization problems with linear equality constraints.

    Main Methods:

    • Development of general SPD formulas using second-order derivative elimination.
    • Analysis of connections and differences among various general SPD formulas.
    • Design of general discrete ZNN models with adjustable parameters for zero stability.
    • Derivation of parameter domains ensuring zero stability.

    Main Results:

    • A comprehensive framework for SPD formulas is presented, including all prior methods.
    • New general discrete ZNN models are proposed for optimization problems.
    • Parameter domains for ensuring zero stability of the discrete ZNN models are identified.
    • Numerical experiments demonstrate the superiority of the proposed methods over conventional approaches.

    Conclusions:

    • The proposed general SPD formulas provide a unified and systematic approach to ZNN discretization.
    • The developed discrete ZNN models offer improved stability and performance, as validated by experiments.
    • The findings advance the practical application of ZNNs in areas like robot motion control.