复杂波网络的控制设计与镇定

项目名称： 复杂波网络的控制设计与镇定

项目编号： No.61503385

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 自动化技术、计算机技术

项目作者： 张雅轩

作者单位： 中国民航大学

项目金额： 20万元

中文摘要： 本项目研究复杂波网络的控制方案设计以及受控网络的稳定性. 波网络是描述弹性系统动力学行为的重要模型，并越来越多地用于精确描述微观系统的动力学行为，其控制与镇定是国际上的热点前沿问题. 对树形等简单波网络已有一些研究结果，但对含有回路、平行边或自环的复杂波网络，结果较少. 本项目将以复杂波网络为研究对象，首先考虑常系数情形，给出网络节点的不同连接条件并建立数学模型；运用状态空间分解法设计网络的控制方案，同时得到网络的渐近稳定性；运用谱分析方法和Riesz基方法进一步研究受控网络是否指数稳定或超稳定；最后将得到的控制方案推广到变系数情形. 本项目旨在对复杂波网络找到一种具体有效的控制方案，研究结果将为工程技术上的网络控制提供参考，并对偏微分网络的控制理论和稳定性理论作有益的补充.

中文关键词： 复杂波网络；控制设计；镇定；状态空间分解

英文摘要： This project is to design the control strategies for complex wave networks and to analyze the stability of the corresponding controlled networks. The wave network is an important model for the dynamic behavior of elastic systems. It is also more and more frequently used to describe the dynamic behavior of many micro-systems. The control and stabilization of wave networks have been intensively investigated recently. Many nice results have been obtained for simple wave networks, such as tree-shaped wave networks. However, there are few achievements about complex wave networks which contain circuits, parallel edges or loops. In this project, such complex wave networks will be considered. We shall first study the networks with constant variables. We determine the connection conditions at each node and construct the mathematical models. Then we use the “state space decomposition method” to design the control strategy and meanwhile obtain the asymptotic stability of the networks. Then we apply spectral analysis and Riesz basis approach to the study of the exponential stability and super-stability of the controlled networks. Finally we generalized the obtained control strategies to wave networks with variable coefficients. The purpose of this project is to find a practical and efficient control strategy for complex wave networks. The results will be helpful for the controller design for networks in industry fields. They will also be useful as a supplementary to the control theory and stability theory of partial differential equation networks.

英文关键词： complex wave network;control design;stabilization;state space decomposition