【作者】 张霞；

【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】 同步问题是复杂网络的一个重要研究方向,得到了越来越多的关注。近年来,几乎所有关于复杂网络同步的研究都是针对单个网络展开的,而现实社会中存在由多个相互作用的网络耦合而成的多网络系统,如不同的基础设施系统耦合而成的基础设施网(水和食物的供应系统、电力系统和交通系统),以及生物种群网等。然而,由于网络之间的相互作用,多网络中网间节点更易出现连接失效现象;此外有些网络具有很强的自我修复能力,即经过一段时间的自我调整,能够恢复正常连接,被称为网间连接可恢复性失效。这种现象不仅会影响网络本身,而且还会破坏与其相连的其他网络的正常工作。本文研究了具有网间节点连接失效的多网络系统的同步控制问题,主要研究内容如下:首先,考虑多网络中网间节点连接具有可恢复性失效的情况,采用伯努利变量来描述连接失效和连接恢复的转换;为了更贴近实际,在多网络数学模型的建立过程中将网络内部和网间耦合项分开表示,并采用维数匹配矩阵处理不同网络节点维数不匹配的问题。进一步,基于牵制控制策略设计了控制器,给出了多网络同步的充分条件。以两个相互耦合的网络为例进行数值仿真,结果表明所设计的控制器能够实现多网络的同步。其次,针对含节点连接可恢复性失效的多网络耦合系统,考虑了由节点间传输导致的时滞和随机扰动等问题,设计了同步控制器,给出了误差系统时滞相关的稳定性条件。并以相互耦合的三网络系统为例进行数值仿真,对比分析了网间节点连接正常和网间连接具有可恢复性失效两种情况的同步效果,结果表明,即便在可恢复性失效的情况下,多网络也能实现各网络内部节点的同步。再次,网间节点连接失效会导致多网络拓扑结构的变化,可将这种变化归结为网络拓扑的切换问题。因此,针对具有切换拓扑的多网络系统,采用平均驻留时间方法,给出了整个网络的全局指数同步条件。进一步选取部分子网络可自同步的多网络进行仿真验证,结果表明,可同步化子网维持同步的总时间满足所给条件,整个网络就可以达到全局指数同步。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】 The synchronization is one of the most important research directions of complex network,which has gained more and more attention.In recent years,almost all complex network research has focused on the single isolated network.But in the real world,there exists the multi-network system constituted by several interacting networks,such as infrastructure network coupled by different infrastructure systems(supply system for food and water,power grid and traffic system),as well as the biological population network,etc.However,due to the interaction between different networks,it may appear the phenomenon of connection failure of nodes between networks;In addition,some network has strong ability to repair itself,and then,the failure of connection can be restored after a period of self-regulation,which can be called the recoverable connection failure.This kind of phenomenon will not only affect the network itself,but also destroy the normal work of the other connected network.Therefore,based on the case of recoverable connection failure of nodes between different networks,synchronization control problem of multi-networks is studied in this thesis,and the main work can be summarized as below:Firstly,considering the recoverable connection failure of coupled nodes between different networks,the synchronization problem of a multi-network is investigated.Bernoulli variable is used to describe the change between failure and recovery events.In order to be closer to reality,coupling terms in the same network and coupling terms between different networks are described separately in the mathematic model.The dimension-transformation matrix is used to deal with the mismatched node dimension.A pinning controller is designed,and the sufficient stability condition is given.Taking the multi-network system coupled by two networks as a simulation example,numerical simulation results show that the proposed controller can achieve synchronization for the multi-network system.Secondly,considering the case of recoverable connection failure of coupled nodes between different networks,the feedback controller is designed for a multi-network coupling system with coupled delay and random disturbance,and then the stability condition of the error system is given.Taking the multi-network system coupled by three networks as a simulation example,through comparing and analyzing the simulation results of normal connection and recoverable connection failure,the result shows that even in the case of recoverable connection failure,the network can realize the synchronization of nodes in each network.Again,the connection failure between nodes in different networks will lead to the change of network topology,and the change can be considered as the switch topology of network.Therefore,for the multi-network with switching topology,the globally exponentially synchronization condition is given by using the average dwell time method.Then,taking the multi-network including networks which can’t realize self-synchronization as a simulation example,the result shows that the global exponential synchronization of the network can be achieved by controlling the synchronization time of the self-synchronized sub-networks.Finally,the main work of this thesis is summarized and some future research directions are put forward.更多还原