求解常数噪声环境下时变非线性方程的离散时间零化神经网络  

Discrete-time zeroing neural network for solving time-varying nonlinear equations with constant noise

作　　者：孙敏 孙洪春[2] 葛静 SUN Min;SUN Hongchun;GE Jing(School of Mathematics and Statistics,Zaozhuang University,277160,Zaozhuang;School of Mathematics,Linyi University,276000,Linyi,Shandong,PRC)

机构地区：[1]枣庄学院数学与统计学院,枣庄市277160 [2]临沂大学数学学院,山东省临沂市276000

出　　处：《曲阜师范大学学报（自然科学版）》2022年第2期47-54,共8页Journal of Qufu Normal University(Natural Science)

基　　金：国家级大学生创新创业训练计划项目(S202110904009);枣庄学院国家自然科学基金预研究项目(102062001)。

摘　　要：该文对有噪声污染但噪声具体表达式未知的时变非线性方程进行研究.首先回顾了一个带积分项的连续时间零化神经网络(continuous-time zeroing nerual network, CT-ZNN),其实质是一个微分-积分方程,可以有效地抑制常数噪声.然后分别利用一步前向差商近似CT-ZNN的导数,利用左(右)矩形公式近似CT-ZNN的积分,得到了3类抗常数噪声的离散时间ZNN算法.进而利用Jury稳定判据给出了离散时间ZNN算法中参数取值范围的估计.最后将所提出的离散时间ZNN算法成功应用到了时变非线性方程问题.This paper intends to study the time-varying nonlinear equations in the environment with noise but no noise specific expression. Firstly, a continuous-time zeroing neural network(CT-ZNN) with integral term is reviewed, which is essentially a differential integral equation and can effectively suppress constant noise. Then, the one-step forward difference quotient to approximate the derivative of CT-ZNN and the left(right) rectangular formula to approximate the integral of CT-ZNN is used, and three discrete-time ZNN algorithms with constant noise tolerance is obtained. Furthermore, the Jury stability criterion is used to estimate the parameter range in the discrete-time ZNN algorithms. Finally, the proposed discrete-time ZNN algorithms are successfully applied to the problem of time-varying nonlinear equations.

关 键 词：时变非线性方程 连续时间零化神经网络 离散时间零化神经网络 

分 类 号：O221.1[理学—运筹学与控制论]