Stabilization For Two Partial Differential Equations

This thesis mainly studies the output feedback stabilization of two kinds of partial differential equations,one is the output feedback stabilization of wave equation with boundary input disturbance under Dirichlet boundary and Neumann boundary conditions respectively,the other is Euler Bernoulli beam equation with periodic disturbance.For the first problem,we adopt a novel robust control method,which is called Uncertainty and Disturbance Estimation(UDE).Based on the UDE method,we filter the input and output of the system to get the disturbance estimation and then compensate the disturbance.Then,we combine the backstepping method to give the controller,and finally make the original system stable.Compared with other existing disturbance compensation methods,UDE method only needs the spectrum information of disturbance.In addition,the feedback control law designed in this paper is easier to operate and realize.For the second kind of problem,by considering the periodic signal as the boundary output of wave equation,we transform the controlled object into a coupled system of beam and wave equation.First,we design a state observer for the coupled system to estimate the disturbance and system state at the same time,and then design output feedback to stabilize the original system.We prove the stability of the system according to the operator semigroup theory.In the end,we give the numerical simulations of main results.