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Random Spatiotemporal Sampled-Data Control for Reaction-Diffusion Neural Networks With Dwell-Time-Based Sojourn

Jinnan Luo, Wanying Wei, Jun Cheng

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    Summary
    This summary is machine-generated.

    This study enhances reaction-diffusion neural network synchronization using a novel switching rule and adaptive event-triggered control. The proposed methods achieve faster convergence and reduce communication costs for stochastic systems.

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    Area of Science:

    • Control Theory
    • Computational Neuroscience
    • Network Science

    Background:

    • Reaction-diffusion neural networks (RDNNs) are crucial for modeling complex spatio-temporal dynamics.
    • Synchronization of RDNNs is challenging due to stochastic switching and communication constraints.
    • Existing methods often require precise transition probabilities or constant sojourn probabilities, limiting their applicability.

    Purpose of the Study:

    • To address the mean-square exponential synchronization of RDNNs under stochastic switching and communication limitations.
    • To develop a more tractable characterization of random mode evolution using dwell-time-dependent sojourn probabilities.
    • To reduce communication burden via a random adaptive event-triggered protocol (RAETP) and a random spatiotemporal sampled-data control (RSTSDC) scheme.

    Main Methods:

    • A dwell-time-dependent sojourn-probability switching rule for characterizing random mode evolution.
    • A random adaptive event-triggered protocol (RAETP) with online threshold adjustment.
    • A random spatiotemporal sampled-data control (RSTSDC) scheme integrating random sampling and switching gains.
    • Derivation of sufficient conditions for mean-square exponential synchronization.

    Main Results:

    • The proposed switching rule offers a more tractable approach to random mode evolution.
    • The RAETP effectively reduces communication load by adjusting triggering thresholds dynamically.
    • The RSTSDC scheme successfully integrates various random elements into the RDNN synchronization framework.
    • Sufficient conditions guaranteeing mean-square exponential synchronization were established.

    Conclusions:

    • The developed methods ensure mean-square exponential synchronization for RDNNs with stochastic switching and communication constraints.
    • The proposed approach demonstrates superior performance in terms of convergence speed and communication efficiency compared to benchmark strategies.
    • This work provides a robust framework for designing controllers for complex neural network systems under realistic operational conditions.