递归多层感知器的稳定性分析——LMI方法  

Stability analysis of recurrent multilayer perceptrons: LMI approach

作　　者：刘妹琴[1] 颜钢锋[1] 

机构地区：[1]浙江大学电气工程学院系统科学与工程学系,浙江杭州310027

出　　处：《控制理论与应用》2003年第6期897-902,共6页Control Theory & Applications

摘　　要：递归多层感知器(RMLP)在工程上应用比较多,但对其稳定性的研究还比较少.本文提出一种新的神经网络模型———标准神经网络模型(SNNM),通过状态空间扩展法,将RMLP转化为SNNM,而SNNM的稳定性分析可转化为一组线性矩阵不等式(LMI)的求解,利用Matlab/LMIToolbox求解LMI,从而判定RMLP的Lyapunov稳定性,并考虑非零阈值对稳定性的影响.该方法也适用于其他类型的递归神经网络(RNN)的稳定性分析.Recurrent multilayer perceptrons (RMLPs) were widely applied to the industrial processes, but stability analysis of RMLPs was seldom researched at present. A novel neural network model named as standard neural network model (SNNM) was advanced. By applying the state space extension method, RMLPs were converted to the SNNMs. Stability conditions of the SNNMs were transformed into some linear matrix inequalities (LMIs). LMIs were solved by Matlab/LMI Toolbox to determine whether RMLPs were Lyapunov stable or not. And the effect of nonzero biased in RMLPs on stability was taken into account. The proposed approach can also be applied to other forms of recurrent neural networks (RNNs).

关 键 词：递归多层感知器 稳定性分析 LMI方法 状态空间扩展法 线性矩阵不等式 标准神经网络模型 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]