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Updated: Apr 20, 2026

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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Optimal control for unknown discrete-time nonlinear Markov jump systems using adaptive dynamic programming.

Xiangnan Zhong, Haibo He, Huaguang Zhang

    IEEE Transactions on Neural Networks and Learning Systems
    |November 25, 2014
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces an adaptive dynamic programming method for optimal control of nonlinear Markov jump systems (MJSs) with unknown dynamics. The approach ensures stability and convergence, validated by simulations.

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    Area of Science:

    • Control Theory
    • Systems Engineering
    • Artificial Intelligence

    Background:

    • Markov jump systems (MJSs) are crucial in modeling systems with abrupt changes.
    • Controlling nonlinear MJSs with unknown dynamics presents significant challenges.
    • Existing optimal control methods often struggle with system uncertainties.

    Purpose of the Study:

    • To develop an optimal control method for discrete-time nonlinear MJSs with unknown dynamics.
    • To address the challenge of approximating system states and solving the Hamilton-Jacobi-Bellman equation.
    • To ensure the stability and convergence of the proposed control approach.

    Main Methods:

    • An identifier is developed to approximate unknown system states.
    • Adaptive dynamic programming is employed to solve the Hamilton-Jacobi-Bellman equation.
    • Neural networks are utilized for approximating the performance index function and control law.

    Main Results:

    • The proposed method successfully approximates system states and solves the HJB equation for nonlinear MJSs.
    • Stability analysis confirms the convergence of the performance index function and the existence of an admissible control.
    • Simulations demonstrate the effectiveness of the optimal control method in linear, nonlinear, and robotic arm cases.

    Conclusions:

    • The developed optimal control method is effective for discrete-time nonlinear MJSs with unknown dynamics.
    • The integration of system identification, adaptive dynamic programming, and neural networks provides a robust solution.
    • The approach offers a promising direction for advanced control applications in uncertain dynamic systems.