【作者】 胡成；

【导师】 蒋海军；

【作者基本信息】 新疆大学 ， 应用数学， 2012， 博士

【摘要】 复杂动力网络系统的同步控制是当今研究复杂网络动力学的重大课题之一,近年来受到了国内外许多学者的广泛关注.本文主要研究几类复杂动力网络在不同控制策略下的同步,包括神经网络的周期间歇控制,无向网络的同步控制,有向网络的自适应间歇控制和社团网络的聚类同步与完全同步控制.第一部分讨论了两类神经网络模型在周期间歇控制下的同步.首先研究了一类具有混合时滞的神经网络的全局指数滞后同步性.通过引入周期间歇控制策略,运用一些典型的分析技巧如反证法、数学归纳法等,建立了系统在无穷范数意义下的全局指数滞后同步准则.其次,考虑了一类具有混合时滞和Dirichlet边界条件的反应扩散神经网络的全局指数同步性.通过对响应网络施加周期间歇控制,利用引进多参数法,Lyapunov泛函技巧,在p范数的基础上得到了系统全局指数同步的充分条件.特别地,在分散型间歇控制下,推出了一个关于控制增益和控制时间率的同步可行域.本节得到的同步判据考虑了扩散强度和扩散空间对网络同步的影响,并明确指出增强神经元的扩散强度或减小扩散空间有利于网络完成同步,反之则不利于网络同步的实现.本章处理的间歇控制策略去除了已有工作中对时滞、控制时间的苛刻限制,推广和改进了前人的工作.第二部分讨论了无向网络的同步控制.首先研究了具有自适应耦合权重的无向网络.结合牵制控制和自适应反馈控制,利用不等式分析方法和Barbalat引理建立了保证网络实现完全同步的判定条件.然后讨论了一类具有分布耦合单时滞的等度网络的间歇控制同步.运用分析方法和不等式技巧,建立了网络全局指数同步的判据.并在此基础上,得到了关于控制增益和控制时间率的同步可行域.与传统的复杂网络同步研究不同,本节处理的同步态不再是网络孤立节点的状态,而是非解耦态,考虑了网络的内联矩阵和节点度对同步状态的影响.第三部分解决了一个在已有工作中提出的开问题,即复杂网络的自适应间歇控制.首先建立了一个有向动力网络模型,指出了它与无向网络在模型表现上的差异.通过对网络部分节点施加分散型自适应间歇控制,运用不等式分析技巧,建立了有向网络实现全局指数同步的判别准则.并根据所得同步判据,推出了一个关于控制时间率的同步可行域.最后,通过两个实例验证了理论结果的正确性和有效性.第四部分研究了两类社团网络模型.首先,考虑了有向社团网络的聚类同步.通过对部分社团分别施加反馈控制和自适应控制,利用Lyapunov稳定性理论,建立了网络实现聚类同步的充分条件.所得结论回答了如下几个具有挑战性的难题：(a)什么样的社团应该优先被控制?(b)至少控制多少个社团才能实现聚类同步?(c)对于受控制的社团,应该选取多大的控制增益才能完成聚类同步?本节研究工作与已有结果的最大不同之处在于在聚类同步处理过程中,每一个社团被视为一个整体来对待,所得聚类同步准则包含了网络社团结构的信息.其次,处理了一类具有传输时滞的加权社团网络的完全同步问题.结合开环控制和反馈控制,通过对耦合强度设计自适应更新律,利用不等式技巧和Barbalat引理,建立了社团网络完全同步到一个预先给定的光滑动力学状态的判定条件.最后,利用数值实例和仿真验证了理论结果的正确性和有效性.更多还原

【Abstract】 Synchronization control of complex dynamical networks is a central topic in theinvestigation of the dynamics of complex networks and has been received much at-tention by a lot of scholars. The aim of this work is to investigate the synchronizationcontrol of several complex dynamic network models, which include the periodicallyintermittent control of neural networks, the synchronization control of undirectednetworks, the adaptive intermittent control for directed networks as well as thecluster synchronization and complete synchronization of community networks.In the first part, the synchronization of two kinds of neural networks is discussedunder periodically intermittent control. First of all, the lag synchronization of neuralnetworks with mixed delays is proposed. By introducing periodically intermitten-t control and applying analysis techniques such as mathematical induction methodand the reduction to absurdity, the criteria for exponentially lag synchronization arederived in terms of the infinite norm. Secondly, the exponential synchronization fora class of reaction-difusion neural networks with mixed delays is considered. Basedon p-norm, the conditions of exponentially complete synchronization are obtainedvia introducing multi-parameters and Lyapunov theory. Especially, a feasible syn-chronization region concerning control gain and the rate of control time is derivedunder a decentralized intermittent control. Besides, the efects of reaction difusionson synchronization are considered and we pointed out that it is beneficial to realizethe synchronization of neural networks when the difusion strengths are strengthenedor the difusion spaces are reduced. It is noted that some traditional restrictions ondelays and work time are removed in our results.The synchronization control of undirected networks is analyzed in the secondpart. First, the models of undirected network with adaptive coupling weights arestudied and the criteria of complete synchronization are given based on pinning con-trol, adaptive feedback laws and Barbalat lemma. In addition, the synchronizationof complex networks with node balance and single coupling distributed delays isdiscussed by using intermittent control. Some conditions are derived to ensure therealization of exponential synchronization by using analysis technique and inequalitymethods. Moreover, a feasible synchronization region for control gains and the rate of control time are also obtained. Diferent from traditional results, the proposedsynchronization states are un-decoupled states and the influence of inner couplingmatrix and the degree of nodes on the synchronized states is included.An open problem, that is, the problem of adaptive intermittent control forcomplex network is solved in third part. First, a model of directed network is es-tablished and the diference on model representations between directed network andun-directed network is pointed out. Some criteria are established to ensure theglobally exponential synchronization by imposing decentralized adaptive intermit-tent control on partial nodes and using inequality techniques. Besides, a feasiblesynchronization region concerning the rate of control time is given. Finally, twonumerical examples are provided to show the validity and efectiveness of the theo-retical results.In the forth part, two type of community networks are investigated. Firstly,the cluster synchronization is proposed via imposing feedback control and adaptivecontrol on partial communities and some sufcient conditions are obtained based onLyapunov theory. In all, this work answers several challenging problems in pinningcontrol of directed community networks:(a) What communities should be chosenas controlled candidates?(b) How many communities are needed to be controlled?(c) How large should the control gains be used in a given community network toachieve cluster synchronization? Unlike the previous results, each community isregarded as a whole and the informations of communities are included in the derivedcriteria. Additionally, the complete synchronization of a delayed community networkis considered in this part. By combining open loop control with feedback control anddesigning adaptive update law for coupling strength, some criteria are established toensure the community networks synchronize onto an any given smoothly dynamicalstate based on inequality techniques and Barbalat lemma. Finally, the validity andefectiveness of the theoretical results are approved by two numerical examples.更多还原