Boundary Control for an Unstable Wave Equation in Annular with Symmetrical Initial Data  

作　　者：齐洁 张晶 

机构地区：[1]College of Information Science and Technology,Donghua University [2]Engineering Research Center of Digitized Textile and Fashion Technology,Ministry of Education,Donghua University

出　　处：《Journal of Donghua University(English Edition)》2016年第3期467-472,共6页东华大学学报（英文版）

基　　金：National Natural Science Foundation Key Program of China(No.61134009);Natural Science Foundation of Shanghai,China(No.16ZR1401200);Fundamental Research Fund for the Central Universities,China(No.2232015D3-24)

摘　　要：A problem of boundary stabilization of a wave equation with anti-damping term in annular is considered.This term puts some eigenvalues of the open-loop system in the right half of the complex plane.Suppose the initial and boundary conditions are rotationally symmetric,the equation in two-dimensional(2-D)annular is transformed to an equivalent one-dimensional(1-D)equation in polar coordinates.A feedback law based on the backstepping method is designed.By a successive approximation,it's proved that there exists a unique solution of the integral kernel which weights the state feedback on boundary.It's also proved that the energy function of the closed-loop system decays exponentially,implying the exponential stability of the closed-loop system.The effectiveness of the control is illustrated with numerical simulations.A problem of boundary stabilization of a wave equation with anti-damping term in annular is considered.This term puts some eigenvalues of the open-loop system in the right half of the complex plane.Suppose the initial and boundary conditions are rotationally symmetric,the equation in two-dimensional（2-D）annular is transformed to an equivalent one-dimensional（1-D）equation in polar coordinates.A feedback law based on the backstepping method is designed.By a successive approximation,it＇s proved that there exists a unique solution of the integral kernel which weights the state feedback on boundary.It＇s also proved that the energy function of the closed-loop system decays exponentially,implying the exponential stability of the closed-loop system.The effectiveness of the control is illustrated with numerical simulations.

关 键 词：boundary control BACKSTEPPING wave equation Lyapunov function ANNULAR 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] O231.2[自动化与计算机技术—控制科学与工程]