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Supplementary Control for Quantized Discrete-Time Nonlinear Systems Under Goal Representation Heuristic Dynamic

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    Summary
    This summary is machine-generated.

    This study introduces a novel neural network (NN) approach for supplementary control of discrete-time nonlinear systems, enhancing stability and performance with quantized communication using goal representation heuristic dynamic programming (GrHDP). The method ensures reliable system operation under communication constraints.

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    Area of Science:

    • Control Systems Engineering
    • Artificial Intelligence
    • Nonlinear Dynamics

    Background:

    • Discrete-time nonlinear systems require robust control strategies, especially with communication constraints.
    • Heuristic dynamic programming (HDP) offers a framework for adaptive control, but its application with quantized data is challenging.
    • Goal representation (Gr) enhances HDP by focusing on specific objectives.

    Purpose of the Study:

    • To develop a supplementary control method for discrete-time nonlinear systems with multiple controllers under quantized communication.
    • To enhance system performance and stability using a novel neural network (NN)-based approach within the GrHDP framework.
    • To address state estimation challenges caused by logarithmic quantization.

    Main Methods:

    • A neural network (NN)-based observer is designed to estimate system states despite quantized communication.
    • A goal representation heuristic dynamic programming (GrHDP) algorithm with a reinforced term is developed for supplementary control.
    • Novel weight updating rules with an additional tunable parameter are constructed for improved NN performance.
    • Lyapunov stability theory is employed to analyze the stability of observer states and NN weights.

    Main Results:

    • The proposed NN-based observer effectively estimates system states in the presence of quantization.
    • The GrHDP algorithm with reinforced learning and novel update rules improves supplementary control performance.
    • Stability conditions for the observer error dynamics and NN weights are rigorously derived.
    • The effectiveness of the developed control strategy is validated through simulations on a power system and a numerical experiment.

    Conclusions:

    • The presented GrHDP-based supplementary control method is effective for discrete-time nonlinear systems with quantized communication.
    • The NN-based observer and novel weight update rules contribute to enhanced system stability and performance.
    • The approach provides a robust solution for control problems involving communication limitations and state estimation.