基于RBF神经网络和移动神经传感单元的分数阶脑机接口系统的泛函区间估计

RBF Neural Network-Based Functional Interval Estimation for a Fractional-Order Brain-Computer Interface System with Mobile Neuro-Sensing Units

摘要: 本文针对未知非线性、有界扰动和测量噪声作用下分数阶脑机接口系统的泛函区间估计问题，提出一种结合RBF神经网络与移动神经传感单元的估计方法。利用RBF神经网络逼近未知非线性，基于移动点测量构造中心状态估计器和误差半径系统，并设计传感单元的投影梯度速度律。通过分数阶Lyapunov方法证明状态估计误差始终位于误差半径包络内，从而保证目标泛函区间估计的可靠性。数值仿真表明，所提方法能够有效包络真实泛函轨迹，且移动点测量相较固定点测量能改善观测位置分布并减小泛函估计区间宽度。

Abstract: This paper addresses the issue of functional interval estimation for fractional-order brain-computer interface systems under the influence of unknown nonlinearities, bounded disturbances, and measurement noise, and proposes an estimation method that combines RBF neural networks with mobile neural sensing units. The RBF neural network is used to approximate the unknown nonlinearities, and a central state estimator and error radius system are constructed based on mobile point measurements; a projection gradient velocity law for the sensing units is also designed. Using a fractional-order Lyapunov approach, it is proven that the state estimation error always remains within the error radius envelope, thereby ensuring the reliability of the target functional interval estimation. Numerical simulations demonstrate that the proposed method effectively encloses the true functional trajectory, and that moving-point measurements improve the distribution of observation locations and reduce the width of the functional estimation interval compared to fixed-point measurements.