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Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
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Finite-horizon control-constrained nonlinear optimal control using single network adaptive critics.

Ali Heydari, Sivasubramanya N Balakrishnan

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    Summary

    A novel Finite-horizon Single Network Adaptive Critic synthesizes optimal controllers for nonlinear systems with control constraints. This single neural network approach provides fixed-final-time solutions, demonstrating effectiveness in complex control problems.

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    Area of Science:

    • Control Theory
    • Artificial Intelligence
    • Nonlinear Systems

    Background:

    • Optimal control for discrete-time nonlinear systems is challenging.
    • Handling control constraints requires sophisticated methods.
    • Existing approaches may lack efficiency or comprehensive solutions.

    Purpose of the Study:

    • To develop a single neural network (NN)-based controller for fixed-final-time optimal control.
    • To address control constraints in discrete-time nonlinear control-affine systems.
    • To provide a computationally efficient and implementable solution.

    Main Methods:

    • A Finite-horizon Single Network Adaptive Critic (FSNAC) is proposed.
    • The FSNAC utilizes a single NN taking system states and time-to-go as input.
    • Control constraints are managed via a nonquadratic cost function.

    Main Results:

    • Convergence proofs for the reinforcement learning training method, training error, and network weights are provided.
    • The controller solves the time-varying Hamilton-Jacobi-Bellman equation.
    • Demonstrated effectiveness in an attitude control problem for a rigid spacecraft.

    Conclusions:

    • The FSNAC offers a fixed-final-time optimal control solution for constrained systems.
    • The single NN formulation simplifies implementation and enables online feedback.
    • The method shows significant potential for practical control applications.