【作者】 张健；

【导师】 井元伟；

【作者基本信息】 东北大学 ， 控制理论与控制工程， 2015， 硕士

【摘要】 复杂网络是具有一定特征和功能的、相互关联相互影响的若干个基本单元所构成的复杂集合体。近年来,复杂网络研究已渗透到数学科学、生命科学、社会科学与工程学科等众多不同的领域,涉及到其中诸多的研究内容。复杂网络的同步就是其中的一个具有代表性的课题。现实世界中,我们处于多个不同网络相互联系的世界中,这些网络之间相互作用,相互依赖,相互影响。因此对多网络的同步行为的研究具有重要的现实意义。本文借助非线性系统理论、稳定性分析理论等知识,对多网络的同步进行了研究,主要工作如下:首先,针对具有不同节点维数的多网络,考虑了网间耦合发生故障的情况,设计了牵制控制器,应用线性矩阵不等式(LMI)方法和Lyapunov稳定性理论,得到了网络同步的充分条件,并给出了牵制控制策略,实现了网络内部节点的同步。并以超Chen系统和Lorenz系统为例进行数值仿真,仿真结果表明所设计的控制器能够实现多网络同步,并且所给出的牵制控制策略比随机牵制策略更有效。其次,考虑了网间耦合不确定的情况,设计了牵制控制器,得到了网络同步的充分条件,实现了网络同步。通过数值仿真可以发现,所设计的牵制控制器能够很好地使网络同步。并且进一步分析了牵制节点的选择与节点强度的关系,分析得出:选择具有较小入强度和较大出强度的节点进行控制有利于网络同步。再次,同时考虑了网络时滞和网间耦合不确定的情况,设计了自适应反馈控制器,得到了网络同步的充分条件。以超Lorenz系统和带时滞的Rossler系统进行数值仿真,仿真结果表明,在具有时滞和网间耦合不确定的情况,所设计的自适应控制器仍能使多网络同步。最后,总结了本文所做的主要工作,对未来的研究方向进行了展望。更多还原

【Abstract】 Complex network is a complex aggregate of some interlinked and interactive units with some characteristics and functions.Recently,complex network has become highly active,with many new systems studied in application areas such as math,biology and computer science.Synchronization is one of the most demonstrating topics in complex networks.In the real world,different networks interconnected constitute the world,between which these networks act on each other,depend on each other and affect each other.Therefore it is significant to study synchronization control problem for multi-networks.In this thesis,combining the nonlinear system theory,control theory and matrix analysis,the synchronization of multi-network is investigated.The main work can be summarized as follows:Firstly,for a class of multi-network with different node dimension in different networks,considering fault in the coupling between the networks,a synchronization controller is designed with pinning control strategy.Based on linear matrix inequalities(LMI)and Lyapunov stability theory,a sufficient stability condition and a pinning control scheme are given by which the nodes in the same network can achieve synchronization.Numerical simulation results show that the proposed controller can achieve synchronization for the multi-network with hyperchaotic Chen system and Lorenz chaotic systems as its nodes.In addition,it shows that the special pinning strategy is more effective than the random pinning strategy.Secondly,for the same multi-network model,considering the uncertain coupling between networks,a pinning controller is designed.Numerical simulation results show the effectiveness of the pinning controller.Then the relationship between the pinned nodes and the coupling strength is analyzed.The result shows that the nodes with low degrees and large degrees are good candidates for applying pinning controllers.Thirdly,for the multi-network system,considering the uncertain coupling between networks,and both coupling delay and nodes delay,an adaptive feedback controller is designed.A sufficient stability condition is given and numerical simulation results show that the proposed controller can achieve synchronization for the multi-network with hyperchaotic Lorenz system and Rossler chaotic systems as its nodes.Finally,the main work of this thesis is summarized and some future research directions are put forward.更多还原