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A Sliding Mode Control Method With Variable Convergence Rate for Nonlinear Impulsive Stochastic Systems.

Penghe He, Huasheng Zhang, Shun-Feng Su

    IEEE Transactions on Cybernetics
    |March 27, 2025
    PubMed
    Summary
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    This study introduces novel sliding mode controllers for nonlinear impulsive stochastic systems (NISSs), enabling adjustable convergence rates and effective jitter suppression. The method ensures finite-time stability for NISSs with variable convergence rates.

    Area of Science:

    • Control Systems Engineering
    • Nonlinear Dynamics
    • Fuzzy Logic Systems

    Background:

    • Existing control methods for nonlinear impulsive stochastic systems (NISSs) often suffer from fixed convergence rates, limiting their adaptability.
    • The problem of variable convergence rate stability in NISSs requires advanced control strategies to meet diverse application demands.
    • Jitter is a common issue in such systems that needs effective suppression for reliable performance.

    Purpose of the Study:

    • To develop a novel methodology for designing sliding mode surfaces for NISSs.
    • To construct a new class of sliding mode controllers capable of achieving variable convergence rate stability.
    • To investigate the jitter suppression capabilities of the proposed controllers and analyze the impact of sigmoid functions.

    Main Methods:

    Related Experiment Videos

    • A sliding mode surface design methodology combining interval stability and T-S fuzzy techniques.
    • Construction of sliding mode controllers utilizing the designed surfaces and sigmoid functions.
    • Derivation of sufficient conditions for finite-time convergence and variable convergence rate stability.

    Main Results:

    • The proposed controllers achieve intelligent adjustment of system convergence rates, overcoming the limitations of fixed rates.
    • Effective jitter suppression is demonstrated, with analysis of different sigmoid functions' effects.
    • Sufficient conditions guaranteeing finite-time state transfer to the sliding surfaces and variable convergence rate stability are established.

    Conclusions:

    • The novel sliding mode control strategy effectively addresses the variable convergence rate stability problem for NISSs.
    • The proposed controllers offer adjustable convergence rates and robust jitter suppression, validated by simulations on a ball-beam system.
    • This approach provides a flexible and powerful tool for controlling complex nonlinear impulsive stochastic systems.