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    This study introduces a novel sliding-mode control scheme for nonlinear systems with unknown disturbances. It uses neural networks for approximate optimal control, ensuring stability and faster responses.

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    Area of Science:

    • Control Theory
    • Nonlinear Systems
    • Artificial Intelligence

    Background:

    • Nonlinear systems often face challenges from unknown mismatched perturbations.
    • Approximate optimal control is crucial for efficient system management.
    • Sliding-mode control offers robust and fast control actions.

    Purpose of the Study:

    • To develop a novel sliding-mode surface (SMS)-based approximate optimal control scheme.
    • To address nonlinear systems affected by unknown mismatched perturbations.
    • To enhance control action speed and system stability.

    Main Methods:

    • Utilizing an observer-based perturbation estimation for online value function updates.
    • Approximating the Hamilton-Jacobi-Bellman equation solution via an SMS-based critic neural network.
    • Implementing nested update laws for asymptotically stable weight error dynamics.
    • Combining sliding-mode control with approximate optimal control design.

    Main Results:

    • The developed scheme effectively handles unknown mismatched perturbations in nonlinear systems.
    • Online updated value functions and asymptotically stable neural network weights were achieved.
    • The integrated sliding-mode and approximate optimal control resulted in faster control actions.
    • Lyapunov's direct method confirmed the stability of the proposed control scheme.

    Conclusions:

    • The novel SMS-based approximate optimal control scheme is effective for nonlinear systems with unknown perturbations.
    • The integration of observer-based estimation and neural networks provides a robust control solution.
    • The method ensures system stability and improves control action speed, validated by simulations.