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    This study introduces an adaptive dynamic programming (ADP) method for optimal control of nonlinear systems. It uses a novel composite critic learning mechanism for efficient policy evaluation and performance optimization.

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    Area of Science:

    • Control Theory
    • Machine Learning
    • Nonlinear Dynamical Systems

    Background:

    • Optimal control of nonlinear dynamical systems is a challenging problem.
    • Existing methods often struggle with computational complexity and stability guarantees.
    • Hamiltonian-based frameworks offer a structured approach to control design.

    Purpose of the Study:

    • To develop an efficient adaptive dynamic programming (ADP) approach for optimal control.
    • To address nonlinear dynamical systems within a Hamiltonian-driven framework.
    • To enhance policy evaluation and performance optimization using novel learning mechanisms.

    Main Methods:

    • Introduced a quasi-Hamiltonian for policy evaluation with admissible policies.
    • Developed a composite critic learning mechanism combining instantaneous and historical data.
    • Defined a pseudo-Hamiltonian to reformulate the Hamilton-Jacobi-Bellman (HJB) equation for online implementation.

    Main Results:

    • Demonstrated theoretical convergence of the adaptive critic design under weakened excitation conditions.
    • Proved the stability of the closed-loop systems.
    • Simulation studies verified the efficacy of the proposed ADP scheme.

    Conclusions:

    • The proposed experience-replay-based ADP provides an efficient solution for optimal control of nonlinear systems.
    • The novel composite critic learning and pseudo-Hamiltonian formulation enable online implementation and improved performance.
    • The method ensures system stability and parameter convergence, validated through simulations.