基于M-矩阵理论的脉冲时滞神经网络稳定性分析与同步控制

发布时间：2018-01-08 14:22

本文关键词：基于M-矩阵理论的脉冲时滞神经网络稳定性分析与同步控制　出处：《电子科技大学》2015年博士论文　论文类型：学位论文

【摘要】：神经网络的研究经过不断发展和完善,现已被成功地应用到计算机科学、人工智能、自动控制、模式识别、图像处理、组合最优化、联想记忆等学科研究领域。而这些应用的关键依赖于神经网络的动力学行为。在实际中,由于时滞的客观存在性和脉冲现象的普遍性,且时滞和脉冲对神经网络动力学行为有着不可忽视的影响。因此,兼具时滞和脉冲神经网络的动力学研究引起了众多学者的关注,并成为非线性系统动力学研究方面的重要课题之一。本文系统地研究了脉冲影响下具有不同时滞类型的几类神经网络的动力学行为。概括地讲,研究内容包括脉冲扰动下平衡点、周期轨的稳定性;脉冲控制下平衡点的指数镇定,脉冲扰动和脉冲镇定下混沌同步控制。具体地讲,本文的研究工作可归纳为如下的六个方面:(一)研究了一类以Hopfield神经网络、细胞神经网络为背景的更一般的神经网络模型在具有连续分布时滞和非线性脉冲干扰下平衡点的稳定性问题。运用拓扑度理论、M-矩阵理论和不等式技巧,获得了保证网络模型平衡点存在性和唯一性的M-矩阵新判据;在该M-矩阵条件下,利用分析的方法证明了网络平衡点在一定的非线性脉冲干扰下仍然能保持全局指数稳定性;通过一个具体例子验证了理论结果的有效性和优越性。(二)作为上述研究内容的继续和深入,进一步讨论了(一)中的神经网络模型在具有变时滞和更具一般性的非线性脉冲扰动下平衡点的稳定性问题。与(一)中所运用到的拓扑度方法不同,基于同胚映射原理,M-矩阵理论和不等式技巧,给出了网络模型平衡点存在且唯一的更一般形式的M-矩阵判定标准;在该M-矩阵条件下,利用分析的方法证明了网络平衡点在更一般非线性脉冲扰动下仍然是全局指数稳定的;通过两个具体例子验证了理论结果的有效性和优越性。(三)研究了一类以神经元的状态直接作为基本变量所得到的静态神经网络模型在具有比例时滞和线性脉冲干扰下平衡点的稳定性问题。这里所考虑的时滞类型既不同于(一)中所讨论的连续分布时滞,也不同于(二)中所考虑的有界变时滞,它是一种无界的时变时滞。基于广义的矩阵测度和推广的Halanay不等式,得到了所考虑网络模型平衡点全局指数稳定矩阵测度形式的判定标准。通过两个具体例子验证了理论结果的有效性和优越性。(四)在原始双向联想记忆(BAM)神经网络的基础上,研究了一类更为复杂(具有周期性变系数和外界输入,连续分布时滞,非线性脉冲干扰和高阶项)BAM神经网络模型的周期振荡动力学行为。基于M-矩阵理论、构造Lyapunov-Krasovskii泛函、不等式技巧和分析的方法,给出了所研究网络模型周期解存在唯一且全局指数稳定的充分条件。通过一个具体例子验证了理论结果的有效性和优越性。(五)研究了一类忆阻神经网络模型(即用新的非线性电子元件忆阻器代替传统神经网络模型中的电阻所得到的一种新的神经网络模型)在脉冲控制下平衡点的镇定性问题。基于脉冲控制的观点,联合运用集值映射和脉冲微分包含理论、非光滑分析及新建立的脉冲微分不等式,给出了所考虑网络模型可全局指数镇定到平衡点零解的代数不等式判定准则。通过两个数值例子验证了理论结果的有效性和可行性。(六)基于两种不同形式的脉冲影响(脉冲扰动和脉冲控制),首先研究了以混沌忆阻神经网络为驱动系统并受到外界脉冲干扰时与其响应系统的同步问题,然后讨论了只在响应系统中加入适当脉冲控制时驱动-响应系统的同步问题。针对这两类问题,综合运用脉冲扰动型和脉冲镇定型的Halanay不等式及前面(二)和(五)中的思想方法,分别获得了状态反馈和脉冲控制下的同步标准。最后,通过一个数值例子验证了这两种同步标准的有效性和可行性。
[Abstract]:The research of neural network through the continuous development and improvement, has been successfully applied to computer science, artificial intelligence, automatic control, pattern recognition, image processing, combinatorial optimization, associative memory and other research fields. The dynamic behavior and the key of these applications depends on the neural network. In practice, due to the universal existence time delay and pulse delay and pulse phenomenon, and has an important influence on the dynamic behavior of the neural network. Therefore, both the kinetics of delay and impulsive neural network has attracted the attention of many scholars, and has become one of the important issue of nonlinear dynamic system. Dynamics with several kinds of neural networks of different types of delay this paper systematically studied the effect of pulse condition. Generally speaking, the research content including pulse disturbance equilibrium, stability of periodic orbits; pulse Under the control of the equilibrium point of exponential stabilization, impulsive perturbations and Impulsive Stabilization of chaotic synchronization control. Specifically, the research work of this paper can be summarized into six aspects as follows: (a) to study a class of Hopfield neural network, the neural network model of general cellular neural network as the background of the continuous distribution delay and nonlinear in the impulsive stability problem under the equilibrium point. By using the theory of topological degree, M- matrix theory and inequality technique, the new criterion of M- matrix to guarantee the existence and uniqueness of the network equilibrium; in the condition of the M- matrix, it is proved that network equilibrium can still maintain global exponential stability in certain nonlinear pulse the interference by using the method of analysis; through a concrete example to verify the validity and superiority of the theoretical results. (two) as to the above research contents and in-depth, further discussed ( A) neural network model with time-varying delays and general nonlinear impulsive stability problem of equilibrium point in it. (a) with different topological method used in the homeomorphism mapping based on the principle of M- matrix theory and inequality technique, gives the network model equilibrium exists and criteria only the more general form of M- matrix; in condition of the M- matrix, it is proved that network equilibrium in pulse more general nonlinear perturbation is globally exponentially stable by using the method of analysis; through two specific examples to verify the theoretical validity and superiority of the results. (three) studied the static neural network a class of models directly to the states of the neurons as the basic variables obtained with proportional delays and linear pulse interference under the stability problem of the equilibrium point. The delay type considered here is different from (a) in the sea Continuous distributed delay theory, but also different from (two) in consideration of the bounded delay, it is a kind of unbounded time-varying delay. Halanay inequalities of matrix measure and generalized based on the network model considering the globally exponential stability of the equilibrium point matrix measure form criteria by two. An example shows the effectiveness and superiority of the theoretical results. (four) in the original bidirectional associative memory (BAM) based on neural network is studied for a class of more complex (with periodic coefficients and external input, continuous distribution delay, nonlinear pulse interference and high order) periodic oscillation dynamics of BAM the neural network model. The M- matrix based on the theory of constructing Lyapunov-Krasovskii functional method and inequality analysis, gives the research cycle network model with sufficient conditions for the existence and uniqueness and global exponential stability. Through a Body examples to verify the validity and superiority of the theoretical results. (five) studied a class of memristive neural network model (the resistance of new nonlinear electronic components memristor instead of the traditional neural network model obtained by a new neural network model) in the impulsive control stabilization problem under equilibrium the pulse control. Based on the view of the joint use of set-valued mapping and impulsive differential inclusions theory, nonsmooth analysis and new impulsive differential inequality, given the network model decidable algebraic inequalities global exponential stabilization to the equilibrium point of the zero solution criterion. Through two numerical examples verify the effectiveness of the theoretical results and feasibility. (six) effects of two kinds of pulse (pulse and pulse control based on disturbance), first studies on chaotic memristive neural network driven system and external interference and pulse response Synchronization of system, and then discusses the synchronization in the response system with appropriate pulse control when the drive response system. According to the two kinds of problems, the integrated use of pulse Halanay inequality and disturbance type and pulse shaping in front of the town (two) and (five) thought method, were given the standard synchronization state feedback and impulsive control. Finally, through a numerical example to verify the effectiveness of the two kinds of synchronization standard and feasibility.

【学位授予单位】：电子科技大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O175

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