振动系统带有干扰时的镇定性研究

项目名称： 振动系统带有干扰时的镇定性研究

项目编号： No.61503276

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： 陈云兰

作者单位： 天津大学

项目金额： 20万元

中文摘要： 本项目研究具有干扰的振动系统的控制器设计及镇定性分析。由偏微分方程描述的振动系统属国际研究热点问题。特别是这些系统具有干扰时备受人们关注，因为众多学科如医学，生物工程，航天科技等领域提出的问题多属干扰问题。尽管对一些具体模型已有某些结果，但到目前为止，关于偏微分方程解的存在性以及解的渐近稳定性，尚无成熟成果。本项目将以弹性系统为研究对象，研究具有干扰时解的存在性及渐近分析。通过设计非线性控制器镇定系统，利用变分方程方法研究解的存在性及唯一性问题，利用Lasalle不变集原理，谱分析方法讨论闭环系统的稳定性问题。

中文关键词： 振动系统；指数稳定性；能量函数；外部干扰；反馈

英文摘要： In this project, we mainly consider the design of the controller and stability analysis to the vibrating system subject to disturbance. The vibration system described by PDE has been received more attention by many mathematicians and engineers. Especially those system   subject to distubance become a very challenging hot issue because of its widely application in medicine, biological Engineering and aerospace and so on. Although there have been a number of results to some concrete model. But so far, there is no mature results about the existence and asymptotic analysis of the solution to the PDE. Based on flexible vibrationsystems, we study the existence and   asymptotic analysis of the solution to the system subject to disturbance. Nonlinear controller is designed to deal with the disturbance and stabilize the system, We use the variational equation methods to prove the existence and uniques of the solution and use the LaSalle invariant set and spectrum analysis to obtain the stability of the closed-loop system.

英文关键词： vibrating system; exponential stability; energy function; external disturbance;feedback