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    This study introduces a novel multigradient recursive (MGR) reinforcement learning scheme for adaptive neural network (NN) control in discrete-time nonlinear systems. The MGR approach overcomes local optima and improves convergence for systems with input saturation.

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    Area of Science:

    • Control Systems Engineering
    • Artificial Intelligence
    • Nonlinear Dynamics

    Background:

    • Traditional adaptive neural network (NN) control methods often suffer from local optimal solutions due to gradient descent weight updates.
    • Discrete-time nonlinear systems with input saturation present significant control challenges, limiting actuator performance and system stability.
    • Existing reinforcement learning schemes may exhibit slow convergence rates in complex control scenarios.

    Purpose of the Study:

    • To develop an advanced adaptive NN control strategy for discrete-time nonlinear systems incorporating input saturation.
    • To address the local optimal problem inherent in gradient descent-based NN training.
    • To enhance the convergence speed and stability guarantees of the control system.

    Main Methods:

    • Employing radial-basis-function (RBF) neural networks for approximating utility functions and system uncertainties.
    • Proposing a multigradient recursive (MGR) reinforcement learning scheme for NN weight updates, utilizing current and past gradients.
    • Applying Lyapunov stability theory to ensure semiglobal uniform ultimate boundedness (SGUUB) of all closed-loop system signals.

    Main Results:

    • The proposed MGR scheme effectively eliminates the local optimal problem associated with traditional gradient descent methods.
    • The MGR approach demonstrates a faster convergence rate compared to standard gradient descent techniques.
    • Stability analysis confirms that all system signals remain semiglobal uniformly ultimately bounded (SGUUB) despite input saturation.

    Conclusions:

    • The novel MGR reinforcement learning scheme provides a robust and efficient solution for adaptive NN control of discrete-time nonlinear systems with input saturation.
    • The proposed method enhances learning efficiency and guarantees system stability, validated through simulation results.
    • This research contributes to the advancement of intelligent control strategies for complex dynamic systems.