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    This study introduces a Bayesian Koopman (B-Koopman) learning algorithm to simplify hysteresis dynamics. The new method offers a linear representation for complex nonlinear systems, improving control and analysis.

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    Area of Science:

    • Control Systems Engineering
    • Nonlinear Dynamics
    • Machine Learning

    Background:

    • Hysteresis dynamics in systems like piezoelectric actuators present challenges due to complex nonlinear models (e.g., Bouc-Wen, Preisach).
    • These complex models limit high-speed and high-precision applications.
    • Effective characterization and control of hysteresis are crucial for advanced engineering operations.

    Purpose of the Study:

    • To develop a novel algorithm for characterizing hysteresis dynamics.
    • To create a simplified, linear model that preserves the essential properties of nonlinear hysteresis systems.
    • To improve the analysis and controller design for hysteresis-affected systems.

    Main Methods:

    • Developed a Bayesian Koopman (B-Koopman) learning algorithm.
    • Established a simplified linear representation with time delay for hysteresis dynamics.
    • Optimized model parameters using sparse Bayesian learning and an iterative strategy.

    Main Results:

    • The B-Koopman algorithm successfully characterizes hysteresis dynamics with a simplified linear model.
    • The proposed method preserves the properties of the original nonlinear system.
    • Parameter optimization via sparse Bayesian learning reduced modeling errors and simplified identification.

    Conclusions:

    • The B-Koopman algorithm provides an effective and superior method for learning hysteresis dynamics compared to conventional models.
    • The simplified linear representation facilitates improved analysis and controller design for hysteresis systems.
    • Experimental validation on piezoelectric positioning confirms the algorithm's practical applicability and performance.