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Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
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    This study introduces an adaptive neural network control for stochastic nonlinear systems using stochastic neural networks to prevent memory overflow. The novel method ensures fixed-time stability and precise tracking within performance bounds.

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    Area of Science:

    • Control Systems Engineering
    • Artificial Intelligence
    • Nonlinear Dynamics

    Background:

    • Existing adaptive stochastic control methods struggle with complex stochastic environments, often facing memory overflow issues due to deterministic approximations.
    • Previous prescribed performance control schemes lack mechanisms to effectively suppress input vibrations and optimize output overshoot and steady-state error bias.

    Purpose of the Study:

    • To develop an adaptive neural network control scheme with prescribed performance for stochastic nonlinear systems.
    • To address the limitations of deterministic neural networks in approximating stochastic nonlinear terms and resolve the memory overflow problem.
    • To introduce a novel prescribed performance design that enhances transient and steady-state characteristics and ensures fixed-time stability.

    Main Methods:

    • Employed stochastic neural networks for approximating stochastic nonlinear terms, overcoming the memory overflow issue.
    • Developed a novel prescribed performance design integrating quadratic and local asymmetric characteristics for vibration suppression and error optimization.
    • Implemented the control scheme within a fixed-time framework to guarantee probabilistic fixed-time boundedness of closed-loop systems.

    Main Results:

    • The proposed stochastic neural network approach effectively resolves the memory overflow issue in adaptive stochastic control.
    • The novel prescribed performance method successfully suppresses transient input vibrations and optimizes output overshoot and steady-state error bias.
    • The fixed-time framework ensures that all closed-loop systems are fixed-time bounded in probability, with tracking errors within predefined bounds.

    Conclusions:

    • The adaptive neural network control scheme with prescribed performance is effective for stochastic nonlinear systems.
    • The use of stochastic neural networks and the novel prescribed performance design offer significant improvements over existing methods.
    • The fixed-time convergence guarantees enhance the robustness and reliability of the control system.