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    Area of Science:

    • Control theory
    • Applied mathematics
    • Computational neuroscience

    Background:

    • Stochastic Markovian reaction-diffusion neural networks are complex systems susceptible to exogenous disturbances and parameter uncertainties.
    • Observer-based control is crucial for stabilizing such systems, but asynchronous operation presents unique challenges.
    • Boundary measurements offer a limited but potentially valuable data source for observer design.

    Purpose of the Study:

    • To develop an observer-based asynchronous boundary stabilization method for stochastic Markovian reaction-diffusion neural networks.
    • To address parameter uncertainties in the drift term and exogenous disturbances.
    • To design a nonfragile asynchronous observer-based boundary controller utilizing only boundary measurements.

    Main Methods:

    • Introduction of a hidden Markov model for asynchronous observer and system modes.
    • Design of a nonfragile asynchronous observer-based boundary controller.
    • Application of inequality techniques and stochastic analysis for stability criteria derivation.
    • Derivation of asynchronous boundary observer and controller gains.

    Main Results:

    • A sufficient criterion for input-to-state exponentially mean-square stability is established.
    • The asynchronous boundary observer/controller gains are explicitly derived.
    • The synchronous observer-based boundary stabilization is presented as a special case.
    • Numerical simulations validate the effectiveness of the proposed method.

    Conclusions:

    • The proposed asynchronous observer-based boundary stabilization is effective for stochastic Markovian reaction-diffusion neural networks with uncertainties.
    • The method demonstrates robustness against exogenous disturbances by utilizing boundary measurements.
    • The derived criteria and gains provide a practical framework for controller design and stability analysis.