Stabilization Of A Class Of Wave Equations With Boundary Disturbance

In this thesis,the active disturbance rejection control(ADRC)is used to study the stabilization problem of one-dimensional wave equation with disturbance and the stabilization problem of variable coefficient wave equation with disturbance.The structure of this paper is as follows:The first chapter is the introduction,which mainly introduces the research background,significance,and practical application scenarios,and gives the research ideas of ADRC and linear extended state observer(LESO).In the second chapter,we discussed the stabilization of one-dimensional wave equation with disturbance.Firstly,the time varying gain observer based on weighted average of measurement displacement is applied to estimate the disturbance,and then the disturbance is eliminated in the feedback loop.Finally,the well-posedness and asymptotic stabilization of the closed-loop are proved by using operator semigroup theory and Lyapunov method.We also provide numerical simulations which demonstrate the results.In the third chapter,the active disturbance rejection control approach is adopted to cope with the stabilization of a variable coefficient wave equation with boundary disturbance.Firstly,the time varying gain observer,instead of the constant gain observer,is applied to estimate the boundary disturbance,and then the disturbance is eliminated in the feedback loop by its estimation.Finally,the well-posedness and stabilization of the closed-loop system are proved by using operator semigroup theory and Lyapunov method.Numerical simulation further validates the conclusion.In the last chapter,the contents of this paper are briefly summarized,and the future development direction is forecasted.