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    Area of Science:

    • Control Engineering
    • Artificial Intelligence
    • Systems Science

    Background:

    • Optimal control of nonlinear discrete-time systems is challenging due to system uncertainties and control constraints.
    • Model Predictive Control (MPC) offers a framework for handling constraints but can be computationally intensive for nonlinear systems.
    • Adaptive Dynamic Programming (ADP) provides a powerful tool for solving complex optimal control problems.

    Purpose of the Study:

    • To develop a functional model predictive control (MPC) approach using adaptive dynamic programming (ADP) for optimal control of nonlinear discrete-time systems.
    • To incorporate the capability of handling control constraints and external disturbances within the proposed control framework.
    • To enhance the robustness and efficiency of nonlinear MPC through an ADP-based strategy.

    Main Methods:

    • A neural-network-based system identification is employed to reconstruct unknown nonlinear discrete-time system dynamics.
    • An actor-critic scheme with a critic network and an action network is utilized for performance function estimation and optimal control input approximation.
    • The infinite horizon optimal control problem is decomposed into a series of finite horizons, with each solved using a finite ADP algorithm subject to constraints and disturbances.

    Main Results:

    • The uniform ultimate boundedness of the closed-loop system is theoretically verified using the Lyapunov approach.
    • Simulations on two distinct cases demonstrate the effectiveness of the proposed ADP-based nonlinear MPC (NMPC).
    • The method exhibits quick response times and strong robustness in handling system uncertainties and disturbances.

    Conclusions:

    • The proposed ADP-based NMPC effectively addresses control constraints and disturbances in nonlinear discrete-time systems.
    • The integration of neural networks and ADP provides an efficient and robust solution for optimal control.
    • The method's performance is validated through simulation, showing significant improvements in response speed and robustness.