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Analysis and Control of Synchronization in Coupled Nonlinear Systems with Time-delays

非线性时滞耦合系统的同步分析与控制

基本信息

批准号：
18560441
负责人：
OGUCHI Toshiki
金额：
$ 2.34万
依托单位：
Tokyo Metropolitan University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2006
资助国家：
日本
起止时间：
2006 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18560441/
关键词：
Control Engineering Time-delays Nonlinear systems Synchronization Chaotic systems

项目摘要

This project has been carried out in two phases.(a) The first phase was to study on synchronization of two coupled nonlinear systems with time-varying delay. In this phase, we introduced the notion of strict semi-dissipativity and showed the convergence property of coupled systems that each system satisfies the strict semi-passive by using the small gain theorem. By using this result, the bounds of the trajectories can be estimated and then a sufficient condition for synchronization can be derived in the form of Linear Matrix Inequalities (LMIs). In addition, in this phase, we proposed a new configuration of anticipating synchronization with the state observer.(b) The second phase was to extend the results in the first phase into N coupled systems. First, we derived a necessary condition under which the synchronization error dynamics has the origin as an equilibrium solution. The obtained condition means that the networks must have symmetric structures. Under the condition, we obtained sufficient conditions for synchronization in unidirectional or bidirectional networks of N chaotic systems with time-delay coupling. The synchronization conditions derived in this project are based on the Lyapunov-Krasovskii theorem in combination with the LyapunoVs indirect method. The obtained conditions were verified by numerical simulations.In this paper we targeted on only complete synchronization of coupled systems and have uncovered a phenomenon of partial synchronization in networks. Therefore the analysis of partial synchronization will be the subject of further research.

该项目分两个阶段进行。(a)第一阶段是研究两个耦合非线性时变时滞系统的同步问题。在这一阶段，我们引入了严格半耗散的概念，并利用小增益定理证明了每个系统满足严格半无源的耦合系统的收敛性。利用这个结果，可以估计的轨道的界限，然后同步的一个充分条件，可以推导出的线性矩阵不等式（LMI）的形式。此外，在这一阶段，我们提出了一种新的配置与状态观测器的预期同步。(b)第二阶段是将第一阶段的结果推广到N个耦合系统。首先，我们推导了同步误差动力学的原点为平衡解的必要条件。得到的条件意味着网络必须具有对称结构。在此条件下，得到了N个时滞耦合混沌系统单向或双向网络同步的充分条件。在这个项目中推导出的同步条件是基于Lyapunov-Krasovskii定理与Lyapunovs间接方法相结合。本文针对耦合系统的完全同步问题，揭示了网络中的部分同步现象。因此，部分同步的分析将是进一步研究的课题。