【作者】 刘凯；

【导师】 王艳红；

【作者基本信息】 沈阳工业大学 ， 系统工程， 2008， 硕士

【摘要】 复杂网络描述了自然界和社会上各种各样的系统,例如,细胞、移动通讯网、计算机网络和互联网等等,人们已经生活在一个充满着各种各样复杂网络的世界中,因此复杂网络的研究愈来愈受到人们的关注,而复杂网络同步问题研究更是其中的热点。人们从很多不同的角度对复杂网络同步问题进行了研究,特别是针对系统含有未知函数或者耦合函数未知时的复杂网络同步研究是其中一项重要内容。因为,任何一个实际系统都具有不同程度的不确定性,例如,所描述的被控对象的数学模型或其环境不是完全确定的,往往包含一些未知因素或随机因素。尽管相关研究已取得了一定成果,然而,现有的研究中考虑节点动力学为滞后情况下的耦合网络的同步以及在现实世界中大量存在的节点动力学具有时延的复杂网络同步问题取得的结果多是局部同步的。本文应用自适应控制理论和李雅普诺夫稳定性理论,分别对不确定动态网络同步问题和节点存在时延的复杂网络自适应同步问题进行研究。针对不确定动态复杂网络的特点,按照参数已知和未知两种情况,分别设计了复杂网络同步控制器和复杂网络同步自适应控制器,给出了相应的实现动态网络渐进同步的充分条件,并进行了理论推导和证明。另外,将上述方法拓展到节点存在时延的复杂网络的同步问题研究中,进一步给出了时滞复杂网络同步的充分条件及理论证明。数值仿真结果表明本文所给出的定理及结论是正确、有效的。更多还原

【Abstract】 Complex networks describe a wide range of systems in nature and society area,such as a cell,a mobile communication networks,a computer network,or the World Wide Web. Since the world we lived is filled of different kinds of complex networks,the research works of complex network have been paid more and more attentions.Especially,the research of the synchronization of complex network is a hot topic.The complex network synchronization problems have been studied from many different perspectives.The study on synchronization of complex network with unknown function or unknown coupling function is one important theme.Since any real system has different degree of uncertainty and the mathematical model describes the object or the description of its environment is not established sufficiently.There have been some research results about synchronization problem achieved in and abroad,however,the time-delay factor widely exists in the real world system has been considered in most existed papers which are locally coupled.In the thesis,the synchronization problem of uncertain dynamical network system has been researched based on Lyapunov stability theorem and adaptive theory.The synchronization controller of complex networks and the adaptive controller of synchronization of complex networks are designed respectively under the circumstances of known parameters and unknown parameters,the sufficient condition of network synchronization is given to guarantee that dynamical network asymptotically synchronize as well as.In addition,the method is used in the research of the synchronization problem about uncertain dynamical network model with time-delay nodes;the sufficient condition of network synchronization is also given to guarantee the time-delay dynamical network can asymptotically synchronize.Numerical simulation results indicate that the proposed theorem and conclusions are correct and effective.更多还原