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    This study introduces adaptive prescribed performance tracking control (APPTC) for articulating cranes (AC) to achieve precise trajectory control despite unknown uncertainties. The novel approach ensures robust performance without approximations, validated through simulations.

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    Area of Science:

    • Robotics
    • Control Systems Engineering
    • Fuzzy Logic Applications

    Background:

    • Articulating cranes (AC) face challenges in precise tracking control due to complex nonlinearities and uncertainties in their multisection arms.
    • Existing control methods struggle with time-variant uncertainties, especially when their bounds are unknown.
    • Fuzzy logic has been explored, but often relies on rule-based systems and approximations.

    Purpose of the Study:

    • To propose an Adaptive Prescribed Performance Tracking Control (APPTC) for articulating cranes (AC).
    • To achieve robust and precise trajectory tracking control in the presence of unknown time-variant uncertainties.
    • To develop an approximation-free control strategy using fuzzy set theory.

    Main Methods:

    • A state transformation is employed to simultaneously achieve trajectory tracking and satisfy prescribed performance criteria.
    • Fuzzy set theory is utilized to model uncertainties without relying on IF-THEN fuzzy rules.
    • Lyapunov analysis ensures deterministic performance via uniform boundedness and uniform ultimate boundedness.
    • An optimal design using a two-player Nash game is formulated to enhance fuzzy-based performance.

    Main Results:

    • The proposed APPTC method demonstrates robust precise tracking control for articulating cranes.
    • The control strategy effectively adapts to time-variant uncertainties with unknown bounds.
    • Deterministic performance is guaranteed through rigorous Lyapunov stability analysis.
    • The optimal design using Nash game theory improves control parameter selection and fuzzy-based performance.

    Conclusions:

    • This research presents the first control strategy for precise tracking control of fuzzy articulating cranes.
    • The APPTC offers an approximation-free and robust solution for complex robotic control tasks.
    • The combination of fuzzy set theory, Lyapunov analysis, and game theory provides a powerful framework for advanced control systems.