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    This study introduces a novel adaptive dynamic programming algorithm to stabilize systems with unknown dynamics and input delays. The method learns a state feedback controller without needing an initial stabilizing controller.

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    Area of Science:

    • Control Systems Engineering
    • Machine Learning
    • Systems Theory

    Background:

    • Stabilization of dynamical systems with unknown dynamics is a significant challenge.
    • Input delays introduce complexity in control system design.
    • Adaptive dynamic programming (ADP) offers a data-driven approach for control problems.

    Purpose of the Study:

    • To develop a robust control algorithm for input-delayed systems with unknown dynamics.
    • To address the challenge of learning controllers from system trajectory data.
    • To eliminate the need for an initial stabilizing controller.

    Main Methods:

    • A value iteration (VI)-based adaptive dynamic programming (ADP) algorithm is proposed.
    • The input-delayed system is transformed into an equivalent delay-free system.
    • The algebraic Riccati matrix equation (ARE) is solved iteratively using basis functions to approximate the controller.

    Main Results:

    • The proposed ADP algorithm successfully learns a state feedback controller for systems with unknown dynamics and input delays.
    • The method effectively solves the ARE without requiring the system model.
    • Basis functions are utilized to satisfy the rank condition of data-constructed matrices.
    • An initial stabilizing controller is not necessary for the algorithm's convergence.

    Conclusions:

    • The developed VI-based ADP algorithm provides an effective solution for stabilizing input-delayed systems with unknown dynamics.
    • The data-driven approach demonstrates practical applicability through illustrative examples.
    • This method advances control strategies for complex systems where model information is unavailable.