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Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
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    This study introduces a novel adaptive optimal control method for nonaffine nonlinear discrete-time systems using value iteration-based Q-learning. The approach effectively solves data-based constrained optimal control problems previously unaddressed.

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    Area of Science:

    • Control Theory
    • Machine Learning
    • Nonlinear Systems

    Background:

    • Reinforcement learning (RL) is effective for optimal control.
    • Constrained optimal control for nonaffine nonlinear discrete-time systems is understudied.
    • Existing methods often require specific performance indices and are limited to linear/affine systems.

    Purpose of the Study:

    • To develop an adaptive optimal control approach for data-based constrained optimal control problems in nonaffine nonlinear discrete-time systems.
    • To overcome limitations of existing methods regarding performance indices and system types.
    • To enable practical application of optimal control to complex nonlinear systems.

    Main Methods:

    • Introduced system transformation with a general performance index to convert constrained to unconstrained problems.
    • Proposed value iteration-based Q-learning (VIQL) to learn the optimal Q-function for the unconstrained problem.
    • Developed a critic-only structure using a single neural network for Q-function approximation and gradient descent for controller design.

    Main Results:

    • Established convergence of the VIQL algorithm with a practical initial condition.
    • Successfully designed an adaptive constrained optimal controller using the learned Q-function.
    • Demonstrated the effectiveness of the method through computer simulations on three distinct examples.

    Conclusions:

    • The developed adaptive control method effectively addresses data-based constrained optimal control for nonaffine nonlinear discrete-time systems.
    • The VIQL algorithm with a critic-only structure provides a viable solution for complex control problems.
    • The approach offers a practical and generalizable framework for advanced optimal control applications.