具有脉冲效应的复值时滞神经网络稳定性分析与控制研究

项目名称： 具有脉冲效应的复值时滞神经网络稳定性分析与控制研究

项目编号： No.61473332

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 其他

项目作者： 赵振江

作者单位： 湖州师范学院

项目金额： 62万元

中文摘要： 近年来，具有脉冲效应和时滞的实值神经网络稳定性分析和控制问题得到了广泛的研究，时滞复值神经网络的稳定性分析也得到了初步的研究。然而，据申请人所知，具有脉冲效应的复值神经网络稳定性分析与控制问题的研究到目前为止还几乎没有报道。本项目拟将研究脉冲时滞复值神经网络的稳定性与控制问题。通过构造脉冲时滞复值神经网络的比较系统，建立比较原理；通过构造复内积空间上的Lyapunov泛函或者Lyapunov-Krasovskii泛函，建立脉冲时滞复值神经网络渐近稳定性与指数稳定性的一系列判定条件。基于建立的脉冲时滞复值神经网络稳定性理论和方法，研究脉冲时滞复值神经网络的同步性、耗散性和无源性的控制问题，通过设计相应的控制器，建立网络同步性、耗散性和无源性的若干判定条件。本项目的完成，不仅丰富和发展了神经网络稳定性理论与方法，而且为复值神经网络在工程领域的应用提供了理论依据。

中文关键词： 复值神经网络；脉冲效应；时滞；稳定性；控制

英文摘要： In recent years, the stability analysis and control for delayed real-valued neural networks with impulsive effects have been widely investigated, and the stability analysis for delayed complex-valued neural networks has been preliminary investigated. However, to the best of the project team personnel's knowledge, there are no reports on the problems of stability analysis and control for delayed complex-valued neural networks with impulsive effects. In this project, the problems of stability analysis and control for delayed complex-valued neural networks with impulsive effects will be investigated. By constructing the comparison system for the delayed complex-valued neural networks with impulsive effects, the comparison principle of stability for the delayed complex-valued neural networks with impulsive effects will be established. By constructing appropriate Lyapunov functionals or Lyapunov-Krasovskii functionals in complex space, some criteria to ensure asymptotical stability and exponential stability for the delayed complex-valued neural networks with impulsive effects will be established. Based on the established stability theory and method for the delayed complex-valued neural networks with impulsive effects, the control problems on the synchronization, dissipativity and passivity for the delayed complex-valued neural networks with impulsive effects will be investigated. By designing appropriate controllers, some criteria to ensure the synchronization, dissipativity and passivity for delayed complex-valued neural networks with impulsive effects will be established, respectively. The obtained achievements in this project will enrich and develop stability theory and method for neural networks, and provide theoretical references for application of complex-valued neural networks in the field of engineering.

英文关键词： Complex-Valued Neural Networks;Impulsive Effect;Time Delay;Stability;Control