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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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Value Iteration Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems.

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    A novel value iteration adaptive dynamic programming (ADP) algorithm solves optimal control problems for nonlinear systems. This method guarantees convergence and introduces new criteria for control law effectiveness.

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    Area of Science:

    • Control Theory
    • Artificial Intelligence
    • Nonlinear Systems

    Background:

    • Optimal control problems for discrete-time nonlinear systems are challenging.
    • Existing adaptive dynamic programming (ADP) methods have limitations in convergence guarantees and control law admissibility.

    Purpose of the Study:

    • To develop a value iteration ADP algorithm for infinite horizon undiscounted optimal control problems.
    • To provide a rigorous convergence analysis for the proposed algorithm.
    • To establish new termination criteria for ensuring the effectiveness of iterative control laws.

    Main Methods:

    • A value iteration ADP algorithm is proposed for discrete-time nonlinear systems.
    • A novel convergence analysis is presented to prove the convergence of the iterative value function to the optimal performance index function.
    • Neural networks are employed for function approximation of the value function and computation of the control law.

    Main Results:

    • The algorithm converges to the optimal performance index function regardless of the initialization function.
    • The iterative value function exhibits monotonic or non-monotonic convergence to the optimum.
    • Admissibility properties of iterative control laws are developed for the first time in value iteration algorithms.
    • New termination criteria are established to guarantee the effectiveness of the control laws.

    Conclusions:

    • The developed value iteration ADP algorithm effectively solves optimal control problems for discrete-time nonlinear systems.
    • The method provides guaranteed convergence and ensures the admissibility and effectiveness of control laws.
    • The use of neural networks facilitates practical implementation, as demonstrated by simulation examples.