基于Wirtinger积分不等式的时滞不确定神经网络无缘算法

发布时间：2018-07-09 14:16

本文选题：Wirtinger积分不等式 + 时滞神经网络　；参考：《西北师范大学学报(自然科学版)》2017年05期

【摘要】：基于Lyapunov稳定性理论,研究了一类含有不确定性的时滞神经网络的鲁棒无缘问题.首先构造含有三重积分项的Lyapunov-Krasovskii(LK)泛函,接着运用一阶和二阶Wirtinger积分不等式来估计LK泛函微分,得到了改善的时滞依赖的无缘条件,这些条件以线性矩阵不等式(LMIs)形式表出.最后,当时滞微分上界分别为0.9和1时,应用折半搜索算法获得了确保不确定时滞神经网络无缘的最大允许时滞上界.运用相对差将所得结果与最新文献结果相比,改善率分别提高了166%和103%,表明文中方法优于现有方法并且有较弱的保守性.另外,当时滞微分上界为0.9时,随机选取10个状态初始向量,利用MATLAB提供的Simulink平台进行系统状态响应曲线的仿真,结果支持所提方法的正确性和有效性.
[Abstract]:Based on the Lyapunov stability theory, the robust miss problem of a class of delayed neural networks with uncertainties is studied. First, Lyapunov-Krasovskii (LK) functional with triple integral term is constructed, then the first-order and second-order Wirtinger integral inequalities are used to estimate the LK functional differential, and the improved delay-dependent conditions are obtained. These conditions are expressed in the form of linear matrix inequalities (LMIs). Finally, when the hysteretic differential upper bound is 0.9 and 1 respectively, the maximum allowable upper bound of delay is obtained by using the half-fold search algorithm to ensure the uncertainty of neural networks with time-delay. By using the relative difference, the improvement rate of the proposed method is increased by 16.6% and 103%, respectively, compared with the results of the latest literature, which indicates that the proposed method is superior to the existing method and has a weak conservatism. In addition, when the upper bound of hysteretic differential is 0.9, 10 initial state vectors are selected randomly, and the simulation of system state response curve is carried out by using Simulink platform provided by MATLAB. The results support the correctness and validity of the proposed method.
【作者单位】：咸阳师范学院数学与信息科学学院;西安电子科技大学机电工程学院;
【基金】：国家自然科学基金资助项目(61501388,11501482) 咸阳师范学院青蓝人才项目(XSYQL201605)
【分类号】：O175

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