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    This study introduces a new adaptive fuzzy tracking control for nonlinear stochastic systems. The method ensures practical predefined-time stability, allowing adjustable settling times for improved control performance.

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    Area of Science:

    • Control Theory
    • Nonlinear Systems
    • Stochastic Systems
    • Fuzzy Logic

    Background:

    • Addresses the challenge of controlling strict-feedback nonlinear stochastic systems with uncertainties and disturbances.
    • Highlights the need for precise and adjustable control over system settling times.

    Purpose of the Study:

    • To develop a practically predefined-time adaptive fuzzy tracking control strategy.
    • To introduce and establish criteria for practically predefined-time stochastic stabilization (PPSS).
    • To enable arbitrary adjustment of system settling time in a mean-value sense.

    Main Methods:

    • Introduced the concept of practically predefined-time stochastic stabilization (PPSS) in the p-th moment sense.
    • Proposed a Lyapunov-type criterion for assuring PPSS.
    • Employed a backstepping design method combined with fuzzy systems to approximate unknown system dynamics.
    • Developed a semiglobal adaptive fuzzy tracking control algorithm.

    Main Results:

    • Successfully designed an adaptive fuzzy tracking control algorithm for the specified class of systems.
    • Demonstrated that the proposed control ensures practical predefined-time stability in the p-th moment sense.
    • Showcased the ability to arbitrarily adjust the settling time, offering enhanced flexibility over existing methods.

    Conclusions:

    • The proposed control strategy effectively addresses the practically predefined-time adaptive fuzzy tracking control problem.
    • The method provides a robust approach for managing stochastic disturbances and uncertainties in nonlinear systems.
    • The arbitrary adjustment of settling time offers significant advantages for practical applications and further research in stochastic control.