带脉冲时间窗口的脉冲神经网络的稳定性分析

发布时间：2018-08-17 17:35

【摘要】：人工神经网络由大量处理单元互联组成的非线性、自适应信息处理系统,在模式识别、图像处理、非线性优化等方面得到了大量的应用。为了描述系统状态的瞬时变化现象,近几年,人们提出了脉冲神经网络并进行了大量的理论研究。目前,大多数对脉冲系统的理论研究主要集中于固定时间的脉冲系统。然而,在实际系统中,脉冲发生的时刻几乎是无法预知的,或者至少是时间相关的。但由于理论分析的复杂性,人们对脉冲发生时刻未预先给定的脉冲系统的研究还很薄弱。为此,本文研究脉冲时刻不能预先确定的脉冲神经网络的定性理论,但为了简化分析,我们假定脉冲发生的时刻局限于一个时间区间内,即每次脉冲的准确触发时刻不确定,但脉冲总发生在确定的时间区间内。我们称这个时间区间为脉冲时间窗口。本文建立了带有脉冲时间窗口的脉冲神经网络模型,并对这些脉冲神经网络模型的稳定性进行分析,得到了一系列确保系统渐近稳定性的充分条件。本论文的主要内容及贡献如下:1.推广固定时间脉冲线性系统,建立了带有脉冲时间窗口的线性脉冲系统模型,并对其稳定性问题进行研究,得到了确保系统渐近稳定的充分条件。2.将脉冲时间窗口概念引入时滞神经网络模型,研究了带有脉冲时间窗口的时滞神经网络的指数稳定性问题,给出了指数收敛率与脉冲时间窗口参数之间的约束关系,并通过数值模拟对理论结果的有效性进行了验证。3.将脉冲时间窗口概念引入切换神经网络,建立了一类更具一般性的混杂脉冲切换神经网络模型,通过理论分析得到了该模型指数稳定的充分条件,并通过数值模拟验证了理论分析的有效性。
[Abstract]:Artificial neural network (Ann) is a nonlinear adaptive information processing system which is composed of a large number of processing units. It has been widely used in pattern recognition image processing nonlinear optimization and so on. In order to describe the transient state of the system, in recent years, impulse neural networks have been proposed and a large number of theoretical studies have been carried out. At present, most of the theoretical researches on impulsive systems are mainly focused on fixed time impulsive systems. In a real system, however, the time at which the pulse occurs is almost unpredictable, or at least time-dependent. However, due to the complexity of theoretical analysis, the study of impulsive systems which have not been given a given pulse time is still very weak. In this paper, we study the qualitative theory of impulsive neural networks, which can not be determined in advance, but in order to simplify the analysis, we assume that the time of pulse occurrence is limited to a time interval, that is, the exact trigger time of each pulse is uncertain. But the pulse always occurs within a given time interval. We call this time interval a pulse time window. In this paper, the impulsive neural network models with impulsive time windows are established. The stability of these impulsive neural network models is analyzed, and a series of sufficient conditions to ensure the asymptotic stability of the system are obtained. The main contents and contributions of this thesis are as follows: 1. A linear impulsive system model with impulsive time window is established by extending the fixed time impulsive linear system. The stability of the system is studied and the sufficient condition of asymptotic stability of the system is obtained. The concept of impulsive time window is introduced into the time-delay neural network model, and the exponential stability of time-delay neural network with impulsive time window is studied. The constraint relationship between exponential convergence rate and parameters of impulsive time window is given. The validity of the theoretical results is verified by numerical simulation. By introducing the concept of impulsive time window into switching neural networks, a more general hybrid impulsive switching neural network model is established. The sufficient conditions for exponential stability of the model are obtained by theoretical analysis. The validity of the theoretical analysis is verified by numerical simulation.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP183

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