Output Feedback Stabilization And Output Tracking Of Heat Equation

In this thesis,we are concerned with output feedback stabilization of a one-dimensional unstable heat equation and output tracking for a one-dimensional heat equation.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 some the main formulas used in this paper.In the second chapter,we are concerned with output feedback stabilization of a onedimensional unstable heat equation.Firstly,Backstepping transform was used to stabilize the unstable heat equation,then estimated the disturbance.then designed a disturbance based observer,then designed the controller,and finally proved the the closed-loop system are exponentially stable and uniformly bounded.In the third chapter,we are concerned with output tracking for a one-dimensional heat equation where the performance output is non-collocated to the control actuation.Firstly,the non-collocated problem is converted into a collocated one by constructing an auxiliary system.Secondly,both the observer and the controller are designed by using the error feedback between the performance output and the reference signal only,which makes the performance output converge to the reference and at the same time,the closed-loop system is uniformly bounded.In the last chapter,the contents of this paper are briefly summarized,and the future development direction is forecasted.