时滞忆阻神经网络的稳定性分析与同步控制设计

发布时间：2018-06-26 22:36

本文选题：忆阻 + 时滞神经网络　；参考：《华中科技大学》2016年博士论文

【摘要】：大脑神经元之间以及神经元与非神经细胞之间通过突触相互连接并实现信息的传递,而忆阻被证实具有类似大脑神经突触在生物电信号刺激下的塑性响应的非线性电学特性,因此可以使用忆阻来模拟突触,构建基于忆阻的神经网络电路.本文通过将忆阻取代传统递归神经网络电路中的电阻从而模拟神经元突触设计了几类关于时滞忆阻神经网络的动力学系统,并研究了其稳定和同步控制问题.这些理论为忆阻元件在神经仿生、信息动态存储和混沌保密通信等方而的应用奠定了理论基础.时滞忆阻神经网络是一类状态依赖的切换系统,不能用经典的针对右端连续的微分方程的稳定性理论和方法来处理.本文通过采用微分包含和集值映射理论,在Filippov右端不连续稳定性理论框架下分析了时滞忆阻神经网络系统的动力学行为,包括无源性、有限时间可镇定性和不可镇定性、自适应同步和一般衰减率同步.以下是本文的主要研究内容：讨论了一类带时变时滞的忆阻神经网络的无源性.与以往文献相比,系统的时变时滞不一定需要可微条件.在此更一般的时滞条件下,本文建立了时滞忆阻神经网络新的基于线性矩阵不等式的无源性条件.理论和仿真结果显示本文的结果比之前文献结果更一般,适用性更广分析了在非线性反馈控制作用下的一类时滞忆阻神经网络的有限时间可镇定性和不可镇定性.这里的非线性控制器具有一般性,针对同一控制器选取不同的参数,分别得到时滞忆阻神经网络的有限时间可镇定性和不可镇定性的基于M矩阵的判据.由于实际工程实践中的操作和效率问题,有限时问稳定控制(镇定)具有极大的现实意义.研究了在自适应反馈控制作用下的一类时滞忆阻神经网络的同步.通过合理引进一个ω(t)函数定义了一个新的误差.由于函数ω(t)的选取的灵活性,本章的同步结果不仅包含了传统的指数和渐近同步,也包含了多项式和对数同步.与线性控制相比,这里采用的自适应控制方法更加符合实际经济利益,避免浪费,同时也能被利用来解决其他时滞系统的同步控制问题.探讨了在非线性反馈控制作用下的一类时滞忆阻神经网络的一般衰减率同步.首先构造了一个关键引理,其包含经典指数稳定性定理作为特殊情况.其次通过设计的非线性控制,最终基于引理得到了时滞忆阻神经网络的的φ型同步(一般衰减率同步)结果.这里的,型同步是在一般框架下,通常线性控制不能实现,事实上它包含指数同步,多项式同步以及其他同步作为特殊情况.
[Abstract]:Neurons in the brain and between neurons and non-neurons connect with each other through synapses to transmit information, while amnesia has been shown to have nonlinear electrical properties similar to the plastic responses of synapses to bioelectrical signals. Therefore, memory can be used to simulate synapses and build a neural network circuit based on memory. In this paper, by replacing the resistor in the traditional recurrent neural network circuit, we simulate the synapses of neurons and design several kinds of dynamic systems about delayed memory neural networks, and study its stability and synchronization control problems. These theories lay a theoretical foundation for the applications of memory elements in neural bionics, information dynamic storage and chaotic secure communication. The delayed amnesia neural network is a class of state dependent switched systems, which cannot be dealt with by classical stability theory and method for the continuous differential equations at the right end. Based on the theory of differential inclusion and set-valued mapping, the dynamical behavior of delayed amnesia neural network systems is analyzed under the framework of Filippov's discontinuous stability theory at the right end, including passivity, finite-time stabilizability and non-stabilization. Adaptive synchronization and general attenuation rate synchronization. The following are the main contents of this paper: the passivity of a class of amnesia neural networks with time-varying delays is discussed. Compared with previous literatures, the time-varying delay of the system does not necessarily require differentiable conditions. In this paper, a new passivity condition based on linear matrix inequality (LMI) is established for the delayed recall neural networks under the more general time-delay conditions. Theoretical and simulation results show that the results obtained in this paper are more general than those obtained in previous literatures. The finite time stabilizability and non-stabilization of a class of time-delay memory neural networks under nonlinear feedback control are analyzed. The nonlinear controller is general here. For the same controller different parameters are selected and the criteria of finite time stabilizability and non-stabilization of delayed amnesia neural networks are obtained respectively based on M-matrix. Due to the problem of operation and efficiency in practical engineering practice, it is of great practical significance to control the stability (stabilization) in limited time. The synchronization of a class of delayed amnesia neural networks under adaptive feedback control is studied. A new error is defined by introducing a 蠅 (t) function reasonably. Due to the flexibility of the selection of 蠅 (t) function, the synchronization results of this chapter not only contain the traditional exponential and asymptotic synchronization, but also include polynomial and logarithmic synchronization. Compared with linear control, the adaptive control method proposed here is more in line with the actual economic benefits, avoids waste, and can also be used to solve the synchronization control problem of other time-delay systems. The general attenuation rate synchronization of a class of delayed amnesia neural networks under nonlinear feedback control is discussed. First, a key Lemma is constructed, which contains the classical exponential stability theorem as a special case. Secondly, based on the Lemma, the 蠁 type synchronization (general attenuation rate synchronization) of the delayed amnesia neural network is obtained by the nonlinear control designed. In this case, the type synchronization is in a general framework, usually the linear control can not be realized, in fact, it includes exponential synchronization, polynomial synchronization and other synchronization as special cases.
【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP183

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