控制理论与应用2024，Vol.41Issue(8)：1459-1468,10.DOI:10.7641/CTA.2023.20776
带有非线性边界和扰动输入的波动方程的输出反馈控制
Output feedback control for wave equations with nonlinear boundary condition and disturbance inputs
摘要
Abstract
The output feedback control of infinite dimensional systems is an important research topic in control theory.Compared with linear boundary input,nonlinear boundary conditions are more applied to practical mathematical models,which can cause various dynamic behaviors,such as chaotic acoustic vibration,period-doubling bifurcation,square wave,and so on.In this paper,the output feedback stability problem of one dimensional wave equation with nonlinear displace-ment boundary condition at left end and total disturbance input at right end is studied.Firstly,the well-posedness of open loop systems is proved by using operator semigroup theory.Secondly,due to the existence of internal nonlinear terms and external disturbances,we prove that the estimator can estimate total disturbances by constructing an infinite-dimensional disturbance estimator.Then,the state observer is designed by means of the measured output signal of the original system,and the stability controller is constructed and the closed-loop system is obtained.Finally,the well-posedness and asymptotic stability of the closed-loop system are proved.关键词
波动方程/非线性边界条件/干扰估计器/输出反馈稳定Key words
wave equation/nonlinear boundary condition/disturbance estimator/output feedback stabilization引用本文复制引用
张亚超,刘军军..带有非线性边界和扰动输入的波动方程的输出反馈控制[J].控制理论与应用,2024,41(8):1459-1468,10.基金项目
山西省基础研究计划(自由探索类)面上项目(20210302123181)资助.Supported by the Basic Research Program of Shanxi Province(Free Exploration)Project(20210302123181). （自由探索类）
