IEEE Trans Neural Netw Learn Syst. 2018 Mar;29(3):597-607. doi: 10.1109/TNNLS.2016.2637567. Epub 2016 Dec 29.
Neural networks (NNs) in the stochastic environment were widely modeled as stochastic differential equations, which were driven by white noise, such as Brown or Wiener process in the existing papers. However, they are not necessarily the best models to describe dynamic characters of NNs disturbed by nonwhite noise in some specific situations. In this paper, general noise disturbance, which may be nonwhite, is introduced to NNs. Since NNs with nonwhite noise cannot be described by Itô integral equation, a novel modeling method of stochastic NNs is utilized. By a framework in light of random field approach and Lyapunov theory, the global asymptotic stability and stabilization in probability or in the mean square of NNs with general noise are analyzed, respectively. Criteria for the concerned systems based on linear matrix inequality are proposed. Some examples are given to illustrate the effectiveness of the obtained results.
在随机环境下，神经网络（NNs）通常被建模为随机微分方程，这些方程由白噪声驱动，如现有文献中的布朗或维纳过程。然而，在某些特定情况下，它们不一定是描述受非白噪声干扰的 NNs 动态特性的最佳模型。本文将一般噪声干扰（可能是非白噪声）引入到 NNs 中。由于存在非白噪声的 NNs 无法用 Ito 积分方程来描述，因此采用了一种新的随机 NNs 建模方法。基于随机域方法和 Lyapunov 理论，分别分析了具有一般噪声的 NNs 的全局渐近稳定性和概率稳定性或均方稳定性。提出了基于线性矩阵不等式的相关系统的准则。通过一些实例说明了所得结果的有效性。
