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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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    This study introduces a Hamiltonian-driven adaptive dynamic programming (ADP) framework for continuous-time nonlinear systems. The method uses a critic network to approximate value gradients, enabling effective optimal control approximation.

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    Area of Science:

    • Control Theory
    • Machine Learning
    • Nonlinear Systems

    Background:

    • Adaptive dynamic programming (ADP) is crucial for optimal control of complex systems.
    • Continuous-time nonlinear systems pose significant challenges for traditional control methods.
    • Existing ADP techniques often struggle with continuous-time formulations.

    Purpose of the Study:

    • To develop a novel Hamiltonian-driven adaptive dynamic programming (ADP) framework.
    • To enable optimal control approximation for continuous-time nonlinear systems.
    • To demonstrate the effectiveness of the proposed Hamiltonian-driven ADP approach.

    Main Methods:

    • A Hamiltonian-driven framework integrating control, policy comparison, and performance improvement.
    • Utilizing the Hamiltonian as a temporal difference for continuous-time systems.
    • Training a critic network to output value gradients for system dynamics analysis.
    • Employing neural network approximation for iterative optimal control approximation.

    Main Results:

    • The Hamiltonian serves as a temporal difference for continuous-time systems.
    • Minimization of the Hamiltonian functional is equivalent to value function approximation.
    • An iterative algorithm with convergence proof for optimal control approximation was presented.
    • Two simulation studies validated the effectiveness of the Hamiltonian-driven ADP.

    Conclusions:

    • The Hamiltonian-driven ADP framework provides an effective approach for continuous-time nonlinear systems.
    • The critic network's value gradient output is key to approximating value derivatives.
    • The proposed method offers a robust solution for optimal control problems in continuous time.