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Robust Standard Gradient Descent Algorithm for ARX Models Using Aitken Acceleration Technique.

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    A new robust and accelerative gradient descent (RA-SGD) algorithm enhances ARX model estimation. This method improves convergence speed and eliminates step-size limitations for more effective model identification.

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    Area of Science:

    • System identification
    • Control engineering
    • Machine learning algorithms

    Background:

    • Standard gradient descent (SGD) algorithms for Autoregressive with Exogenous inputs (ARX) models suffer from slow convergence and step-size sensitivity.
    • These limitations hinder the efficiency and robustness of parameter estimation in dynamic systems.

    Purpose of the Study:

    • To develop a robust and accelerative standard gradient descent (RA-SGD) algorithm for ARX models.
    • To improve the convergence rate and eliminate step-size dependency of the gradient descent method for ARX model identification.

    Main Methods:

    • The proposed RA-SGD algorithm incorporates the Aitken acceleration method.
    • Convergence analysis and simulation examples are used to validate the algorithm's performance.

    Main Results:

    • The RA-SGD algorithm achieves at least quadratic convergence, significantly improving upon the linear convergence of standard SGD.
    • The algorithm demonstrates robustness and consistent convergence regardless of the step size.
    • Simulation results confirm the effectiveness of the RA-SGD algorithm.

    Conclusions:

    • The developed RA-SGD algorithm offers a robust and efficient solution for parameter estimation in ARX models.
    • Aitken acceleration effectively enhances the convergence properties of gradient descent for system identification tasks.