带输入饱和的耦合波方程的边界反馈镇定  

Boundary Feedback Stabilization of Coupled Wave Equations with Input Saturation

作　　者：武洁琼[1] 任倩 WU Jieqiong;REN Qian(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,太原030006

出　　处：《河南科学》2020年第1期25-32,共8页Henan Science

基　　金：国家自然科学基金(11801339);山西省留学人员科技活动项目择优资助项目(2018-172)。

摘　　要：考虑通过位移耦合的波方程的边界状态反馈控制问题.假设边界状态反馈控制具有输入饱和约束.首先引入一个辅助系统消除输入饱和约束的影响,然后应用Lyapunov函数方法设计边界反馈控制器,证明闭环系统的指数稳定性.此外,借助Galerkin方法证明闭环系统解的存在唯一性.该结果推广了已有文献中关于单个波系统边界反馈镇定性的结果.The boundary state feedback control problem of the wave equations coupled by displacement is considered.The boundary state feedback control assumed to have an input saturation constraint.First,an auxiliary system is introduced to eliminate the influence of input saturation constraint.The boundary feedback controller is designed based on the method of Lyapunov function and the exponential stability of the closed-loop system is proved.Besides,the existence and the uniqueness of the closed-loop system solution is proved by Galerkin method.Our results generalize the previous results of the boundary feedback stabilization for a single wave system in the existing literature.

关 键 词：耦合波方程 输入饱和 边界状态反馈 指数稳定 闭环系统稳定性 LYAPUNOV函数 

分 类 号：O175.27[理学—数学]