【作者】 郭丽琳；

【导师】 王燕舞；

【作者基本信息】 华中科技大学 ， 控制理论与控制工程， 2009， 硕士

【摘要】 复杂动力学网络的控制与同步研究是目前国内外关于复杂网络研究的热点问题之一。在实际的复杂动力学网络中,由于结构的建模误差、环境温度和湿度等外部条件的变化、通信流量的随机性等因素的影响,复杂动力学网络中的随机和不确定因素是客观存在的,而且有时是无法忽略的。因此,建立保守性小的随机或不确定复杂动力学网络模型并根据模型的变化改变分析综合所采用的方法及工具是有必要的。鉴于此,本文致力于研究随机和不确定因素下的复杂动力学网络的控制与同步问题,这对理解和应用复杂网络有重要的意义。论文建立了带马尔可夫模式依赖时延的不确定无向离散复杂动力学网络模型,运用奇异系统并结合变量变换的方法,基于线形矩阵不等式,得到了带马尔可夫模式依赖时延的无向离散网络随机稳定的充分条件。针对一种连续时间、参数和时延服从马尔可夫切换的复杂动力学网络模型,论文借助奇异系统的方法,构造了新的Lyapunov泛函结合耦合的线性矩阵不等式,得到了该复杂动力学网络随机稳定的充分条件。论文提出了另一类连续马尔可夫切换时延复杂动力学网络模型,即参数、时延和内部耦合矩阵都服从马尔可夫切换的情况,运用Kronecker积的性质结合构造的Lyapunov泛函,得到了连续时间马尔可夫切换时延网络指数均方同步的充分条件。论文还研究了随机非线性耦合时变时延动力学网络,其中,耦合项为一个布朗运动形式的随机扰动项。基于Lyapunov稳定性定理、It微分方程、不变微分方程的LaSalle不变原理,运用自适应反馈控制从理论上研究并得到了这类网络均方同步的充分条件。更多还原

【Abstract】 Control and Synchronization of complex dynamical networks with stochastic and uncertain factors is one of the most famous problems in the world. In the real world, because of existence of the structure error, the influence caused by the change of the environment temperature and humidity and the random factor in information traffic, the stochastic and uncertain factors of complex dynamical network exist, and can not ignored sometimes. Therefore, it is necessary to build stochastic or uncertain complex dynamical network model with low conservative property and change the analysis methods and tools according to the change of the model. Accordingly, the control and synchronization of complex dynamic networks with stochastic and uncertain factors are analyzed, which is meaningful for the understanding and application of complex networks.Based on liner matrix inequality, undirected discrete Markovian time-dependent delay dynamical network model has been researched by using descriptor system approach combining with variable transformation method. The sufficient condition for the stability of undirected discrete Markovian time-dependent delay network can be obtained.A continuous Markov jump delay network dynamical model is introduced, which consists of Markov jump mode-dependent delays and parameters. The stability and synchronization have been analyzed by using descriptor system approach and the sufficient condition of the stability of continues-time Markov jump delay network can be obtained. Another continuous Markov jump delay network dynamical model is presented, namely, parameters, delays and inside coupling matrix are all subjected to Markov jump. Combining the property of Kronecker product with the Lyapunov functional, the sufficient condition of exponential mean square synchronization of continues-time Markov jump delay dynamical network can be obtained.The synchronization problem of time-varying delay network with stochastic nonlinear coupling has been investigated by using adaptive feedback control strategy. In this model, the random coupling factor is a random disturbance in the form of Brown motion. Based on Lyapunov stability theorem, It differential equation and LaSalle invariable differential equation theory, the sufficient condition for the synchronization of this network has been obtained by using adaptive feedback control.更多还原