Output Tracking And Stabilization Of A Class Of Wave Equation

Based on trajectory planning and spectrum analysis,this paper studies the output tracking and stabilization of a class of wave equations.The structure of this paper is as follows:The first chapter is the introduction.This chapter mainly introduces the research background,significance and previous related achievements,and gives the research ideas of trajectory planning and spectrum analysis.In the second chapter,this paper considers the output tracking of a class of wave equations,in which the reference signal is a harmonic signal,the control and performance output are non-collocated.First design the state observer in terms of the output to estimate the state of the system.Then using the estimated state,the controller is designed to make the performance output to track the given reference signal and keep all states of the closed-loop system bounded.In the third chapter,the stability of one-dimensional wave equation is considered.According to the theory of operator semigroup,the well posedness of the solution of the equation is proved.With reference to [1],the spectral analysis of the equation is carried out and the stability conditions of the system are obtained.