Output Regulation And Disturbance Rejection For Infinite-dimensional System

In this thesis,we study output regulation and disturbance rejection for infinite-dimensional systems.For external disturbance with dynamic model,a basic method to deal with output regulation/disturbance rejection is the well known internal model principle which assumes that the disturbance information and reference information are generated by an external autonomous system called exosystem.This leads to include unstable mode of the exosystem in feedback controller.This thesis expands mainly the internal model principle from three aspects.First,in chapters 2 and 3,we consider output regulation with general reference signals or general disturbance signals which can not be handled by the internal model principle.Output regulation for a wave equation with general disturbances and non-collocated control and output configuration is discussed in chapter 2.Chapter 3 is devoted to output regulation for a wave equation with general disturbances and reference signals.Except the boundedness hypothesis,the “general disturbance signal” is supposed to be completely unknown.Compared with the internal model principle,the main features of our controllers are as follows: a)The disturbance is estimated,which is not needed usually by the internal model principle where the disturbance signals are almost known except the unknown initial value of the exosystems.By observer based approach,the internal model principle may estimate nominal system state and disturbance.b)Servo system is designed to generate reference signals or regulating signals,which is different from the exosystem by the internal model principle.In chapters 4 and 5,the finite-dimensional exosystems are extended to infinite-dimensional exosystems and time-varying exosystems.A stabilization problem for a wave equation with boundary input or boundary output periodic disturbance which can be regarded as a boundary output of an autonomous one-dimensional wave equation is considered in chapter4.The traditional internal model principle is usually not capable of solving output regulation problem for infinite-dimensional exosystems with unbounded output.Using the properties of coupled wave system,we design an observer-based feedback control law and prove that the stability of the wave equation depends on the period of periodic disturbance.In chapter 5,we study robust output regulation for a heat equation with general time-varying exosystems.Compared with the existing results,the condition of time-varying exosystems is relaxed.In the last chapter,chapter 6,we study dynamic feedback controller design.Dynamic feedback has shown to be necessary for robust output regulation by the internal model principle.Inspired by the fact that the observer-based feedback control is a special dynamic feedback,we design three dynamic feedback controllers for second order infinite-dimensional systems in chapter 6,which satisfy another second order finite-dimensional system or infinite-dimensional system.It is shown that when the dynamic feedback is in the control space,the closed-loop system is asymptotically stable if and only if Hautus condition holds;If the dynamic feedback is not in the control space,the Hautus condition is necessary but not sufficient for the asymptotic stability;If the dynamic feedback law is almost the same as the original system where the dynamic feedback law can be regarded as an observer for the original system,the closed-loop system is exponentially stable if and only if the original system is exactly controllable.