基于边界位移量测的一维波方程的稳定性  

Stabilization of a One-dimensional Wave Equation Based on Boundary Displacement Observation

作　　者：武晓辉[1] 李胜家[1] WU XIAOHUI, LI SHENGJIA(School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Chin)

机构地区：[1]山西大学数学科学学院

出　　处：《应用数学学报》2018年第2期268-279,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(61174082,11671240,61503230)资助项目

摘　　要：本文考虑一类非同位波方程的控制问题，提出了一个新的基于观测边界位移的时滞反馈控制器．通过算子半群理论和Riesz基逼近的方法，证明了相关闭环系统的适定性和稳定性，并给出系统指数稳定时的条件．数字模拟进一步验证了结论的成立．In this paper, the stabilization of a one-dimensional wave equation with non- collocated observation at its unstable free end and controller at another end is considered. A novel output feedback control law with a constant time-delay only based on boundary displacement observation is proposed. The well-posedness of the close-loop system is proved by using operator semigroup theory and Riesz basis theory. The condition which guarantees the exponential stability of the closed-loop system can be determined. The result＇s relevance is illustrated with a numerical simulation.

关 键 词：RIESZ基 指数稳定 反馈控制 时间延迟 波方程 

分 类 号：O175.2[理学—数学]