忆阻系统的同步及其控制研究

发布时间：2018-02-10 21:38

本文关键词： 忆阻系统 Lorenz系统双复合同步混合控制随机混沌系统分布时变时滞脉冲系统间歇随机扰动控制周期噪声宽度随机忆阻神经网络微分包含　出处：《华南理工大学》2016年博士论文　论文类型：学位论文

【摘要】：忆阻是华人电路理论专家蔡少棠教授首次提出的概念.忆阻器被假设为与电量和磁通量相关的,消失的非线性无源二终端电路元件.自其被提出后的近四十年间,忆阻的研究几乎没什么突破性进展.直到2008年,惠普实验室制作出第一款忆阻器,其便引起了许多科研人员的注意,迅速地成为了自动化等相关领域最热门的研究方向之一.忆阻对流经其的电流或两端的电压具有独特的记忆功能,其应用前景十分广泛,如在保密通信、存储器、人工智能计算机等众多领域都具有巨大的潜在应用价值.据目前已有的文献来看,国际上对忆阻的研究主要集中在两个方面:(1)按照惠普实验室研究的思路,研究如何以最经济实惠的材料制作出具有忆阻特性的器件;(2)按照蔡少棠教授的思路,研究由忆阻构建的系统的动力学行为及其应用.本文按照蔡少棠教授的思路,继续对忆阻系统的动力学行为及其应用进行了更深入的研究,包括忆阻系统的同步以及控制.研究的对象涉及已有大量文献报道的忆阻神经网络和忆阻混沌系统等.笔者还考虑了忆阻系统与随机系统相结合,如利用间歇随机扰动镇定忆阻混沌系统;忆阻系统与不连续系统理论相结合进一步研究了忆阻系统的动力学性质.我们利用动力系统理论的一些基本工具,如Lyapunov稳定性理论、Hanalay不等式、脉冲理论等现代控制理论方法,也将利用随机系统的Lyapunov稳定性理论等随机系统中的常用方法.通过对上述问题和方法的研究,建立了忆阻系统的同步以及控制研究的基本结构,在忆阻的理论和应用的研究上取得了一定进展.本文的主要贡献阐述如下:1.介绍了忆阻的相关背景、研究意义和现状,着重阐述了忆阻神经网络和忆阻混沌系统的研究进展,简单介绍了与本文相关的理论知识.2.基于四个混沌系统的组合-组合同步和复合同步,研究了一种六个忆阻Lorenz系统的新型双复合同步.利用Lyapunov稳定性理论和状态反馈控制方法,得到了确保结论成立的充分条件,并且进行了相应的理论证明和数值仿真,验证了我们的同步设计方法的有效性和可行性.由于所设计的同步复杂性更高,因此在通讯应用中,传递和接收信号的安全性更好.3.研究了基于忆阻Lorenz系统的离散和分布时变时滞随机混沌系统的混合控制问题.首先,基于由分段线性忆阻建模的Lorenz系统,提出了一个随机切换混沌系统.其次,设计一个新型混合控制器,并建立保证相应的随机系统平凡解均方指数稳定的判据.此外,本文提出了一个新技术,解决了两个不同时刻所对应的状态值之差的问题,而这两个时刻之间可能存在脉冲时刻,其对应的状态值之差不能直接用随机Newton-Leibniz公式来刻画.最后,给出数值例子证明了设计方法的有效性和可行性.4.考虑了基于间歇布朗噪声扰动对一个给定的非线性系统的镇定与消稳问题.首先,给出了一些与控制周期T和噪声宽度δ相关的新型稳定性与不稳定性判据和结论.随后利用所得到的结果研究基于间歇随机扰动的镇定与消稳,并且把所获得的理论应用于忆阻混沌系统的镇定问题.最后给出两个数值例子验证了我们的理论.5.研究了基于分布脉冲控制的随机时滞忆阻神经网络的指数同步问题.根据忆阻的特性,建立了相应的驱动随机忆阻神经网络和具有分布脉冲控制输入的响应随机忆阻神经网络,再利用同步的概念和随机微分包含理论得到了同步误差系统.利用广义脉冲时滞微分不等式方法,我们得到同步误差系统均方指数稳定的判据,即驱动系统和相应系统达到指数同步的判据.最后给出了数值仿真验证了所得理论结果的有效性.最后,总结本文工作,展望后续课题.
[Abstract]:The memristor is the concept of Professor Cai Shaotang Chinese expert circuit theory is proposed for the first time. The memristor is assumed to be associated with electric and magnetic flux, nonlinear passive two terminal circuit elements disappear. Since nearly forty years after it was brought forward, the research of memristor hardly what breakthrough. Until 2008, HP Labs produced the first paragraph of the memristor, it has attracted many researchers attention, quickly became one of the most popular research direction of automation and other related fields. The memristor has a unique memory function of voltage or current flowing through the ends, which is widely used in secure communication, such as, memory, have potential applications in many fields such as artificial intelligence computer. According to the current literature, international research on the memristor is mainly concentrated in two aspects: (1) according to the HP lab study The way, study how to use the most affordable materials to produce devices with memristor characteristics; (2) according to Professor Cai Shaotang's ideas, research by the dynamic behavior of the system construction of the memristor and its application. In this paper, according to Professor Cai Shaotang's ideas, continue on the dynamic behavior of the memristor system and its application are further studied the system includes the memristor and synchronization control. The research object involved has been reported the memristor chaotic memristive neural network and system. The author also considered memristive systems and stochastic systems combined, such as the use of intermittent random disturbance stabilization of memristor chaotic system; memristive system and discontinuous system theory. With the further study of the dynamics of the memristor system. We use some basic tools such as dynamic system theory, Lyapunov stability theory, Hanalay inequality, the theory of modern control theory of pulse The method, commonly used methods in stochastic systems will use stochastic systems with Lyapunov stability theory. Through the research on the problems and methods, establish the synchronization of memristor system and the basic structure of control research, the research on the theory and application of the memristor has made great progress. The main contribution of this paper are as follows: 1. introduces the related background of memristor, significance and research status, focuses on the research progress of memristive neural network and memristor chaotic system, introduced the.2. theory knowledge and the related four chaotic systems were combined synchronization and complex synchronization based on study of a six memory a new double composite resistance Lorenz system synchronization. By using Lyapunov stability theory and state feedback control method, the sufficient condition to ensure the conclusion, and the proof of theory and numerical simulation, test Validity of the synchronous design method and feasibility of our design. Because the synchronization complexity is higher, so in the communication application, mixed control problem for transmitting and receiving signals better.3. security of discrete and distributed memristor Lorenz system based on time-varying stochastic chaotic systems with time delay. First, by Lorenz system piecewise linear memristor based modeling, this paper presents a random chaotic system. Secondly, the design of a new hybrid controller, and establish the criterion of the trivial solution of the corresponding stochastic system to ensure the exponential stability in mean square. In addition, this paper presents a new technique to solve the corresponding two different time value the problem of poor, and may always exist between the two pulse time, the corresponding status difference cannot be directly used to describe the random Newton-Leibniz formula. Finally, a numerical example is given to prove the design The effectiveness and feasibility of the.4. method considering the stabilization of nonlinear systems for a given between Xiebulang noise disturbance and elimination based on stability problems. First of all, gives some new stability and control cycle T and noise width delta associated with instability and conclusion. Then by use of the result of stabilization and blanking interval based on the random disturbance, and the problem of theory for memristor chaotic system stabilization. Finally two numerical examples are given to verify the theoretical.5. we studied the random delay distribution of impulse control memristive neural network based on exponential synchronization problem. According to the characteristics of memristor, established the corresponding random drive memristive neural network with distributed control input and pulse response of random memristive neural network, then use the concept of synchronization and random differential synchronization error system includes theory By using the generalized delay differential inequality method. We get the criterion of pulse synchronization error system exponentially mean square stable, and corresponding system drive system to achieve the criterion of exponential synchronization. Finally, the validity of the numerical simulation of the obtained theoretical results are given. Finally, the work of this paper and prospects for future research.

【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TN60;TP273

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