【作者】 张伟；

【导师】 李传东； 宋乾坤；

【作者基本信息】 重庆大学 ， 计算机科学与技术， 2015， 博士

【摘要】 非线性系统的不连续控制一直是控制领域的热门话题,其中神经网络的不连续控制在这些年得到了很大的关注。时滞神经网络的不连续控制系统主要包含了多种右端不连续系统,其中包括脉冲控制的时滞神经网络系统、切换时滞神经网络系统、间歇控制神经网络系统等混杂控制系统。近年来,时滞神经网络也在图像处理、模式识别、联想记忆、信号处理、全局优化和保密通信等领域得到广泛的应用。因此,对时滞神经网络不连续控制的研究是非常重要的研究课题。尤其是时滞神经网络在随机扰动、脉冲控制、间歇控制、切换等混合作用下的动力学属性得到深入的研究,且取得了一些重要成果。本文主要工作集中于分析:线性耦合随机神经网络、惯性BAM神经网络、非线性耦合随机神经网络、忆阻神经网络的稳定性和同步,其主要内容和创新之处可概述如下:①研究了线性耦合随机时滞神经网络的稳定性和同步。主要分为两部分:一部分我们考虑了切换和脉冲控制作用在耦合随机时滞神经网络中,得到了一个新的脉冲微分等式,并构造了一个误差系统,再通过利用Lyapunov稳定性理论、比较原则和线性矩阵不等式技术得到了该系统的同步标准;另一部分,我们集中讨论了马尔科夫切换、随机扰动、时滞脉冲混合作用下的时滞神经网络的动力学属性,首先,一些新的、一般的条件得到了推导,通过建立一个扩展的Halanay微分不等式到脉冲动力系统中,其次,利用了M矩阵的性质讨论了该网络的同步问题,免除了传统构建一个误差系统的繁琐,最后我们得到了有效条件确保同步依赖于耦合时滞脉冲的条件,展现了耦合和脉冲作用下神经网络能够达到同步。②研究了不连续控制的另外一种形式,即间歇控制。本文中分为两部分讨论了间歇控制,一部分考虑的是间歇控制是周期性的,另一部分考虑的是非周期性的。在第四章中,我们主要考虑的是周期间歇控制作用下,对一个二阶系统进行稳定性研究。我们利用数学变换,将二阶惯性BAM神经网络转化成为一个一阶系统,这样我们就能很容易的进行研究和探讨,再通过构建一个通用Lyapunov函数和矩阵不等式技术,最终我们得到了非线性系统稳定的充分条件。在第五章中,研究了非线性耦合随机神经网络的同步问题,设计合理的非周期的间歇控制器,找到一个合理的非线性耦合假设条件,和得到同步误差系统的稳定性条件,从而实现非线性耦合随机神经网络的渐近同步;另外,设计了一个合理的自适应规则,在这种规则下使非线性耦合随机神经网络在非周期间歇控制下也能够得到同步的充分条件。③研究了当下比较热门的话题,即忆阻器神经网络,当忆阻器实体最终实现,那么将会带来科技的又一次革命。在阅读大量相关文献的基础上,我们构建了一个线性耦合的忆阻时变时滞递归神经网络的复杂网络模型。并且探讨了该系统在时滞脉冲和间歇控制两种不连续控制作用下的稳定性和同步。设计了有效的时滞脉冲控制器,得到了同步误差系统的稳定性条件;另外,利用M矩阵方法,在外部控制和时滞脉冲双重控制作用下使得该网络能够达到指数同步。同时,我们也设计了周期间歇控制的控制器,得到了耦合忆阻时变时滞递归神经网络的稳定性和同步的有效条件。根据分析,得到了周期间歇控制参数的可行域,为控制器的设计提供了更好的数值基础。更多还原

【Abstract】 Discontinuous control of nonlinear systems has been a hot topic in the field of control. Recently, as special class of discontinuous control of nonlinear systems, discontinuous control of neural networks with delayed gets a lot of attention. Discontinuous control of delayed neural networks mainly consists of a variety of right discontinuous systems, such as: neural network systems with delayed under impulsive control, switching neural network systems with delayed, neural network systems via intermittent control hybrid control systems. Recently, delayed neural networks have been applied in many fields, such as image processing, pattern recognition, associative memory, signal processing, optimization, and secure communication. Therefore, the research of discontinuous control of delayed neural networks is a very important topic. Especially, dynamics behavior of delayed neural networks was thorough studied under the hybrid effects of stochastic perturbation, impulsive control, intermittent control, system switching, and obtain some important results.The dissertation focuses on analysing stability and synchronization of neural networks, such as: linear coupling stochastic neural network, nonlinear coupling stochastic neural network, memristor-based neural network, and inertial BAM neural network. The main contributions and originality contained in this dissertation are as follows:① Stability and synchronization of linear coupling neural networks with time-vary delay and stochastic perturbations were presented. It is divided into two parts: 1) we consider coupled switched delay neural network with stochastic perturbation and impulsive effects, got a new impulsive differential equation, and constructed an error systems. Based on the Lyapunov functional method, the comparison principle, and linear matrix inequality technology, we drived some sufficient synchronization conditions of nonlinear system; 2) in the second part, we focusesed on analysis dynamics of the hybrid effects of Markovian switching, stochastic perturbation, impulsive delay on neural networks. First, some novel generic criteria for Markovian switching neural networks with stochastic perturbation and impulsive delay were derived by establishing an extended Halanay differential inequality on impulsive dynamical systems. Second, based on M matrix method, we discussed synchronization of the network, and avoided building an error system. Last, our sufficient conditions ensuring the synchronization are dependent on coupling and impulsive delay and show coupling and impulsive effects on the syn-chronization of neural networks.② We investigated another form of discontinuous control: intermittent control. This paper is divided into two parts invistgated intermittent control: the part considers intermittent control is aperiodically, and the other periodically. In chapter 4, we study global exponential stability problem for inertial BAM neural networks with time-varying delay via periodically intermittent control. By utilizing suitable variable substitution, the second-order system can be transformed into first-order differential equations. We can obtain effective condition of exponential stability of nonlinear system by constructing a common Lyapunov functional, and using linear matrix inequality. In the fifth chapter, stability of nonlinear coupled neural networks with time-vary delay and stochastic perturbation is studied. Stability condition of synchronization error system was obtained, ensuring the asymptotic synchronization of nonlinear coupled neural networks with time-vary delay and stochastic perturbation, by designing appropriate aperiodically intermittent controller, and finding a reasonable assumption of nonlinear coupled. In addition, in order to realize synchronization of neural network through adaptive aperiodically intermittent control, we designed reasonable updating laws.③ Recently, memristor-based neural networks have attracted increasing attention. When memristor realized successfully, it will be a revolution in science and technology. Based on previous research, we constructed complex network model of a linear coupled memristor-based neural recurrent networks with time-vary delay, where stability and synchronization were investigated under discontinuous control of delay impulsive and intermittent. By constructing effective impulsive delay controller, obtained stability condition of synchronization error system. In addition, exponential synchronization of the nonlinear system was invistigated by utilizing M matrix method, and under external and delay impulsive dual control. Meanwhile, we also designed a periodically intermittent controller, and obtained the stability and synchronization efficient condition of coupled memristor-based recurrent neural networks with time-varying. According to the analysis, we have got feasible region of intermittent control parameters, which the designing of the controller provided a better numerical foundation.更多还原