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Fuzzy Intermittent Control for Nonlinear Coupled Delayed PDE-ODE Systems.

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    This study presents a fuzzy intermittent control method for complex nonlinear systems with delays, ensuring stability using Takagi-Sugeno models and Lyapunov functions. The approach is validated for controlling hypersonic rocket cars.

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    Area of Science:

    • Control Theory
    • Nonlinear Systems
    • Fuzzy Logic

    Background:

    • Nonlinear coupled delayed partial differential equation-ordinary differential equation (PDE-ODE) systems present significant control challenges.
    • Spatially averaged measurements (SAMs) offer a practical approach for system monitoring.

    Purpose of the Study:

    • To develop a fuzzy intermittent control method for nonlinear coupled delayed PDE-ODE systems.
    • To ensure the exponential stability of these complex systems.

    Main Methods:

    • Modeling the systems using the Takagi-Sugeno (T-S) fuzzy PDE-ODE model.
    • Designing fuzzy intermittent controllers based on a switching Lyapunov functional (LF).
    • Utilizing space-dependent linear matrix inequalities (SDLMIs) to establish stability conditions.

    Main Results:

    • Sufficient conditions for exponential stability were derived.
    • The proposed fuzzy intermittent control method demonstrated effectiveness.
    • The control strategy was successfully applied to a hypersonic rocket car (HRC) model.

    Conclusions:

    • The fuzzy intermittent control method provides a robust solution for stabilizing nonlinear coupled delayed PDE-ODE systems.
    • The use of T-S fuzzy models and Lyapunov functionals is effective for this class of systems.
    • The approach is practical and validated through simulations on a complex application.