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    Area of Science:

    • Control Theory
    • Fuzzy Systems
    • Stochastic Systems

    Background:

    • Nonlinear stochastic switching models present control challenges due to parameter uncertainties and complex dynamics.
    • Semi-Markovian parameters and incomplete kernels add further complexity to system analysis and controller design.
    • Interval Type-2 Fuzzy (IT2F) models offer a robust framework for handling uncertainties in nonlinear systems.

    Purpose of the Study:

    • To develop a novel sliding mode control (SMC) strategy for discrete nonlinear stochastic switching models.
    • To address challenges posed by semi-Markovian parameters and incomplete semi-Markovian kernels (SMK).
    • To design an IT2F SMC law capable of ensuring stability and reducing chattering.

    Main Methods:

    • Utilizing an interval type-2 fuzzy (IT2F) model to characterize nonlinear system dynamics.
    • Employing a mode-dependent Lyapunov function and incomplete SMK for stability analysis.
    • Developing an IT2F SMC law incorporating a learning strategy.

    Main Results:

    • Sufficient conditions for ensuring the stability of sliding dynamics under the specified conditions were derived.
    • The proposed IT2F SMC law effectively guides state signals to the sliding region.
    • Mode switching-induced chattering was significantly reduced.

    Conclusions:

    • The developed IT2F SMC strategy provides a robust solution for controlling discrete nonlinear stochastic switching models.
    • The method effectively handles uncertainties and incomplete information within the system.
    • Simulation results for a truck-trailer model validate the efficacy of the proposed control strategy.