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Stabilization and Synchronization of Neural Networks via Impulsive Adaptive Control.

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    This study introduces an impulsive adaptive control strategy for stabilizing and synchronizing coupled neural networks (NNs). The novel approach uses adaptive impulsive gains, improving performance over fixed-gain methods.

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    Area of Science:

    • Control Theory
    • Computational Neuroscience
    • Systems Engineering

    Background:

    • Coupled neural networks (NNs) present challenges in stabilization and synchronization.
    • Traditional impulsive control methods often rely on fixed gains, limiting adaptability.

    Purpose of the Study:

    • To develop and analyze an impulsive adaptive control (IAC) strategy for coupled NNs.
    • To address limitations of fixed-gain impulsive control by introducing adaptive gain updating.

    Main Methods:

    • Designed a novel discrete-time adaptive updating law for impulsive gains.
    • Developed impulsive adaptive feedback protocols for stabilization and synchronization.
    • Performed convergence analysis for the proposed control strategy.

    Main Results:

    • Established several criteria for stabilization and synchronization of coupled NNs using IAC.
    • Demonstrated that the adaptive updating law maintains performance at impulsive instants.
    • Validated the theoretical results through two comparative simulation examples.

    Conclusions:

    • The proposed IAC strategy effectively achieves stabilization and synchronization in coupled NNs.
    • The adaptive gain updating mechanism offers advantages over traditional fixed-gain methods.
    • The study provides a robust framework for controlling complex neural network systems.