几类复杂动态系统的稳定性、镇定及其同步控制

发布时间：2018-01-03 19:34

本文关键词：几类复杂动态系统的稳定性、镇定及其同步控制　出处：《华南理工大学》2016年博士论文　论文类型：学位论文

【摘要】：在现实系统及其外部环境中不可避免的存在时滞现象、脉冲现象、随机现象和非线性等情形.要真实地描述实际问题,更准确地反映自然与社会工程系统的动态特性,常常用到大系统或者复杂系统.复杂系统被广泛应用于工程技术、神经网络、生态学及控制论等各个领域之中.因此,含有非线性、时滞、脉冲、随机现象等因素的复杂系统的稳定性及控制理论是当前的一个研究热点.本文以非线性脉冲神经网络、时滞随机系统、带有扩散项的网络系统为研究对象,对这些系统的稳定性、镇定及同步控制等进行了探讨.本论文的主要工作分为以下几个方面:1.介绍大系统或复杂系统产生的历史、研究背景、意义,综述了国内外研究的现状及发展状态,并对目前时滞问题、脉冲问题、同步控制问题等方面所采用的方法、困难进行了阐述与分析.2.考虑了无界时滞的网络情形,即具有比例时滞的脉冲Cohen-Grossberg神经网络,并对激励函数和时滞函数条件进行弱化,利用脉冲不等式和数学分析的技巧,得到系统平衡解是全局渐近稳定性和一致渐近稳定性的一些充分条件,所得结论具有一定的广泛性.最后,通过举例和数值仿真来进行验证.3.研究了一类非线性多时滞积分微分系统的耗散性和稳定性,先给出了一个比较广泛的Halanay不等式,再利用稳定性理论和分析技巧,结合自己所提出的广义Halanay’s不等式分别对三种不同情形的积分微分系统进行了研究,得到了系统具有耗散性和稳定性的充分条件.最后通过两个例题及其仿真来进行验证.4.从随机干扰和脉冲控制两个方面研究了混合变时滞Cohen-Grossberg神经网络的同步控制问题,通过控制器及设置的更新律,利用稳定性理论和分析技巧,得到驱动系统和响应系统可同步控制的一些充分条件.最后通过举例和数值仿真证明了所提出的方法的有效性。5.研究了带反应扩散项的神经网络的同步控制,主要从周期间歇自适应反馈控制、脉冲控制两种方法使得驱动系统和响应系统达到同步控制的目的.通过构造Lyapunov函数,利用稳定性的相关理论及泛函微分方程的不变原理等来进行证明所得的结论.在证明过程中,通过wirtinger’s不等式及带脉冲形式的halanay不等式等技巧,使得复杂系统在化简过程中变得相对简单些.最后通过举例来验证所得的结论.6.基于图论、随机微分方程的基本知识,结合Lyapunov函数和分析技巧,首先研究了在随机干扰下的多组耦合系统的稳定性,得到相应p阶矩指数稳定性和几乎必然指数稳定的充分条件.紧接着采用时滞反馈和非线性脉冲控制器研究多组耦合系统镇定的问题,得到均方指数稳定性的充分条件.最后通过举例来验证所得结论的有效性和正确性.最后,在总结全文的基础上,对未来工作进行了展望.
[Abstract]:In the real system and its external environment, there are inevitable delay phenomena, impulsive phenomena, stochastic phenomena and nonlinear situations. More accurately reflect the dynamic characteristics of natural and social engineering systems, often used in large systems or complex systems, complex systems are widely used in engineering technology, neural networks. Therefore, there are nonlinear, time-delay and impulses in the fields of ecology and cybernetics. The stability and control theory of complex systems with stochastic phenomena and other factors are currently a hot topic. In this paper, nonlinear impulsive neural networks, time-delay stochastic systems, network systems with diffusion terms as the research object. The stability, stabilization and synchronization control of these systems are discussed. The main work of this paper is as follows: 1. The history, research background and significance of large or complex systems are introduced. In this paper, the current situation and development of research at home and abroad are reviewed, and the methods used in time delay problem, pulse problem and synchronization control are also discussed. The difficulties are described and analyzed .2. the impulsive Cohen-Grossberg neural network with proportional delay is considered in the case of unbounded delay. The conditions of excitation function and delay function are weakened, and some sufficient conditions for the global asymptotic stability and uniformly asymptotic stability of the equilibrium solution of the system are obtained by using impulse inequality and mathematical analysis techniques. Finally, the results are verified by examples and numerical simulations. Finally, the dissipation and stability of a class of nonlinear integro-differential systems with multiple delays are studied. In this paper, a general Halanay inequality is given, and then the stability theory and analytical technique are used. Three kinds of integro-differential systems under different conditions are studied in combination with the generalized Halanay's inequality proposed by us. The sufficient conditions for the system to be dissipative and stable are obtained. Finally, two examples and their simulations are used to verify the results. 4. The mixed variable delay Cohen-Gr is studied from two aspects: random disturbance and pulse control. Synchronization control problem of ossberg neural network. Through the controller and the updated law of setting, the stability theory and analytical skills are used. Some sufficient conditions for synchronous control of drive system and response system are obtained. Finally, the effectiveness of the proposed method is proved by examples and numerical simulations. 5. The synchronization control of neural network with reaction diffusion term is studied. . Mainly from the periodic intermittent adaptive feedback control, pulse control two methods to drive system and response system to achieve the purpose of synchronous control. Through the construction of Lyapunov function. By using the theory of stability and the invariant principle of functional differential equation, the conclusion is obtained. By means of wirtinger's inequality and halanay inequality with impulses, etc. Make the complex system in the process of simplification become relatively simple. Finally, through an example to verify the conclusion. 6. Based on graph theory, the basic knowledge of stochastic differential equations. Combined with Lyapunov function and analytical technique, the stability of multi-group coupled systems under random disturbances is studied. The sufficient conditions for the exponential stability and almost inevitable exponential stability of the corresponding p-moment are obtained. Then the problem of stabilization of multi-system coupled systems is studied by using time-delay feedback and nonlinear impulsive controller. A sufficient condition for the stability of the mean square index is obtained. Finally, the validity and correctness of the conclusions are verified by examples. Finally, based on the conclusion of the paper, the future work is prospected.
【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】：O231

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