Boundary Control Of Coupled Reaction-Diffusion Systems

This thesis explores the boundary controlling problem of coupled reaction d-iffusion systems with heat exchange in boundary according to Fourier's laws.The coupling system is the coupling of ordinary differential equations and partial dif-ferential equations.The reaction diffusion equations include the reaction,diffusion and convection terms.The system can be used in industrial production and rep-resents mechanical coupling and coupling of chemical reactions and other issues in industrial production.Dealing with the boundary control problem of the coupled linear reaction dif-fusion system with heat source,in this paper,the Backstepping method is used to derive the kernel equation.Firstly,introduce a reversible Volterra transformation,to transform the original system into a target system which is exponentially sta-ble;then find the transformation which is introduced,and at last prove that the close-loop system is exponentially stable with the transformation introduced and it's inverse.Compared with the existing results,the main work of this thesis is to solve the system with heat exchange in boundary based on Fourier's laws.The existing results are the coupling between ordinary differential equations and one-dimensional partial differential equations.This thesis deals with the coupling between ordinary differential equations and multidimensional partial differential equations.