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    Area of Science:

    • Control Systems Engineering
    • Applied Mathematics
    • Nonlinear Dynamics

    Background:

    • Nonlinear coupled systems involving partial differential equations (PDEs) and ordinary differential equations (ODEs) present significant control challenges.
    • Existing control methods may not adequately address the complexities of sampled-data control for such hybrid systems.
    • Takagi-Sugeno (T-S) fuzzy models offer a framework for representing and controlling nonlinear systems.

    Purpose of the Study:

    • To develop a sampled-data fuzzy control strategy for nonlinear coupled PDE-ODE systems.
    • To ensure exponential stability of the closed-loop system under discrete-time measurements.
    • To provide a systematic design method based on linear matrix inequalities.

    Main Methods:

    • Modeling the nonlinear coupled PDE-ODE system using a Takagi-Sugeno (T-S) fuzzy approach.
    • Designing a sampled-data fuzzy controller incorporating ODE state feedback and PDE static output feedback.
    • Utilizing a novel time-dependent Lyapunov functional for stability analysis.
    • Formulating the stabilization condition via linear matrix inequalities (LMIs).

    Main Results:

    • A novel sampled-data fuzzy controller was designed for the nonlinear coupled PDE-ODE system.
    • The proposed controller guarantees exponential stability for the closed-loop system.
    • The design methodology, based on LMIs, provides a computationally tractable solution.
    • Simulation results for a hypersonic rocket car demonstrate the controller's effectiveness.

    Conclusions:

    • The developed sampled-data fuzzy control approach effectively stabilizes nonlinear coupled PDE-ODE systems.
    • The use of a time-dependent Lyapunov functional and LMIs offers a robust design framework.
    • The method is validated through practical application in a hypersonic vehicle control scenario.