忆阻器神经网络的无源性与同步问题

发布时间：2018-10-09 20:34

【摘要】：对人类中枢神经系统的模仿促成了神经网络概念的出现,虽然大多数神经网络只能模仿出其复杂生物原型的一部分,但在解决实际问题中已经十分有效。基于非线性分析理论,该论文研究了忆阻神经网络的无源性及同步控制问题。主要结论如下:(1)讨论了具有混合延时的忆阻神经网络的指数无源性问题。通过构建合适的Lyapunov函数和使用新的函数处理技术,忆阻神经网络的指数无源性标准转变为四个线性矩阵不等式,而线性矩阵不等式可以很容易通过LMI工具箱进行验证。此外,在Lyapunov函数构造中,引入了非正定矩阵使结论更加合理。(2)论述了具有混合延时的忆阻神经网络的自适应指数同步问题。使用Lyapunov方法设计了一个具有反馈控制律的自适应控制器来实现指数同步。这个自适应控制器新颖、简单且可适用于具有不同忆阻器数学模型的神经网络,并且在同步标准中,无需解线性矩阵不等式或者代数公式等条件。(3)研究了具有混合延时和不同时间尺度的忆阻竞争神经网络的自适应同步问题。通过数学符号替换简化了忆阻器竞争神经网络,使其更适宜数学运算。设计了一个间断的状态反馈控制器来达到系统的同步,此同步控制器同样简单有效。在数值仿真中使用正反例子对定理条件中激励函数有界性和全局Lipschitz连续性要求进行了分析。
[Abstract]:The imitation of human central nervous system leads to the emergence of the concept of neural network. Although most neural networks can only imitate a part of its complex biological prototype, it is very effective in solving practical problems. Based on the theory of nonlinear analysis, the passive and synchronous control problems of amnesia neural networks are studied in this paper. The main conclusions are as follows: (1) the exponential passivity problem of amnesia neural networks with mixed delay is discussed. By constructing appropriate Lyapunov function and using new function processing technique, the exponential passive criterion of recall neural network is transformed into four linear matrix inequalities, which can be easily verified by LMI toolbox. In addition, in the construction of Lyapunov function, the nonpositive definite matrix is introduced to make the conclusion more reasonable. (2) the adaptive exponential synchronization problem of amnesia neural networks with mixed delay is discussed. An adaptive controller with feedback control law is designed by using Lyapunov method to realize exponential synchronization. This adaptive controller is novel, simple and suitable for neural networks with different mathematical models of amnesia, and in the synchronization standard, There is no need to solve linear matrix inequalities or algebraic formulas etc. (3) the adaptive synchronization problem of memory competitive neural networks with mixed delay and different time scales is studied. By replacing the mathematical symbols, the competitive neural network of the resistive device is simplified, which makes it more suitable for mathematical operation. A discontinuous state feedback controller is designed to achieve the synchronization of the system. The synchronization controller is also simple and effective. In the numerical simulation, the boundedness of the excitation function and the requirement of global Lipschitz continuity in the theorem condition are analyzed by positive and negative examples.
【学位授予单位】：燕山大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O231;TP183

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