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    This study introduces an optimal guaranteed cost sliding mode control for nonlinear systems with disturbances. Approximate dynamic programming and neural networks ensure system stability and control performance.

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    Area of Science:

    • Control Systems Engineering
    • Nonlinear Dynamics
    • Artificial Intelligence

    Background:

    • Constrained-input nonlinear systems are susceptible to matched and unmatched disturbances.
    • Integral sliding mode control and approximate dynamic programming (ADP) offer potential solutions for robust control.
    • Existing methods may not fully address optimal guaranteed cost control under complex disturbances.

    Purpose of the Study:

    • To design a novel optimal guaranteed cost sliding mode control for constrained-input nonlinear systems.
    • To address systems affected by both matched and unmatched disturbances.
    • To ensure system stability and minimize costs under uncertainties.

    Main Methods:

    • Integral sliding mode control theory combined with approximate dynamic programming (ADP).
    • Transformation of the control problem into an auxiliary system with a modified cost function.
    • Application of a single-critic neural network (NN) based ADP algorithm for approximate optimal control.
    • Lyapunov techniques to prove neural network weight error convergence and system stability.

    Main Results:

    • An optimal guaranteed cost sliding mode control law was derived using ADP and NN.
    • The control scheme effectively handles matched and unmatched disturbances in nonlinear systems.
    • Lyapunov stability analysis confirmed the uniform ultimate boundedness of the sliding mode dynamics.
    • Simulation results demonstrated the feasibility and effectiveness of the proposed control strategy.

    Conclusions:

    • The developed control scheme provides robust and optimal guaranteed cost performance for constrained nonlinear systems.
    • The integration of integral sliding mode control and ADP offers a powerful approach for complex control problems.
    • The method ensures system stability despite external disturbances and input constraints.