Euler-Bernoulli梁方程基于边界分数阶导数反馈控制的镇定  

Stabilization of Euler-Bernoulli beam equation via boundary fractional derivative feedback control

作　　者：周华成[1] 寇春海[2] 

机构地区：[1]中国科学院数学与系统科学研究院,北京100190 [2]东华大学理学院,上海201620

出　　处：《应用数学与计算数学学报》2015年第2期211-221,共11页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(2011CB808002)

摘　　要：研究具有边界控制的Euler-Bernoulli梁方程基于边界分数阶导数反馈控制的镇定问题.首先,给出开环系统在Salamon意义下的适定性;其次,运用半群方法和LaSalle不变原理,证明了闭环系统生成C_0-半群并且闭环系统是渐近稳定的;最后,设计了一个未知输入类型的状态观测器,其观测器状态渐近收敛于原系统的状态.The stabilization of an Euler-Bernoulli beam equation with boundary control via fractional derivative feedback control is considered. The well-posedness of the open loop system in the sense of Salamon is first proved. By semigroup methods and the LaSalle invariance principle, it is shown that the resulting closed- loop system is associated with C0-semigroup and is asymptotically stable. As a consequence of this asymptotical stability result, an unknown input type state observer is designed that is convergent asymptotically.

关 键 词：Euler-Bernoulli梁方程 分数阶导数 边界反馈控制 C0-半群 LaSalle不变原理 

分 类 号：O231[理学—运筹学与控制论]