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Discrete-Time Stable Generalized Self-Learning Optimal Control With Approximation Errors.

Qinglai Wei, Benkai Li, Ruizhuo Song

    IEEE Transactions on Neural Networks and Learning Systems
    |April 1, 2017
    PubMed
    Summary
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    A new stable generalized policy iteration (GPI) algorithm explicitly considers approximation errors for nonlinear optimal control. This adaptive dynamic programming approach ensures convergence for control systems with potential errors.

    Area of Science:

    • Control Theory
    • Nonlinear Systems
    • Adaptive Dynamic Programming

    Background:

    • Optimal control problems for nonlinear systems are crucial in many engineering applications.
    • Existing algorithms often struggle to account for approximation errors inherent in iterative methods.
    • Generalized Policy Iteration (GPI) offers a framework for adaptive dynamic programming but requires explicit error handling.

    Purpose of the Study:

    • To develop a stable Generalized Policy Iteration (GPI) algorithm that explicitly incorporates approximation errors.
    • To provide a unified structure for discrete-time iterative adaptive dynamic programming and reinforcement learning algorithms.
    • To analyze the properties and convergence guarantees of the GPI algorithm in the presence of approximation errors.

    Main Methods:

    Related Experiment Videos

    • Development of a stable GPI algorithm designed for infinite horizon optimal control of nonlinear systems.
    • Explicit mathematical formulation and analysis of approximation errors within the GPI framework.
    • Establishment of admissibility criteria for approximate iterative control laws and convergence criteria for errors.

    Main Results:

    • The developed stable GPI algorithm provides a general structure for discrete-time adaptive dynamic programming and reinforcement learning.
    • Admissibility of the approximate iterative control law is guaranteed when approximation errors meet specific criteria.
    • Convergence of the iterative value function to a finite neighborhood of the optimal performance index is established under defined error conditions.

    Conclusions:

    • The novel GPI algorithm effectively handles approximation errors in nonlinear optimal control.
    • The algorithm offers a unified framework for various iterative learning and adaptive control methods.
    • Demonstrated convergence and admissibility provide theoretical guarantees for practical applications.