Stabilization Of Partial Differential Systems With Non-local Term

In control theory,the stabilization problem of partial differential systems with nonlocal terms is a very classic problem,which has always been of interest to sci-entific researchers.Such problems have become more and more widely used in practice.This thesis will study the given partial differential system with nonlocal terms.The full text is divided into four chapters.In the first chapter,we introduce the background of the partial differential system stabilization problem with nonlocal terms,the current status of research at home and abroad,and give relevant preliminary knowledge.In the second chapter,we first consider the vibration behavior of a transport equation with a nonlocal term μu(x0 t).For the boundary state feedback stabiliza-tion problem of the transport equation at internal points,we use the well-known Backstepping method to design the state feedback controller to make the original system and the target system equivalent.Designing an output feedback controller based on an infinite-dimensional observer,we choose the appropriate state space H,define the system operator,using the operator semigroup theory we prove that the closed-loop system is exponentially stable.Finally,we give numerical simulations to verify our conclusions.Secondly,in the case of coupling with two ODEs,we consider the boundary state feedback stabilization problem of the transport equation with the nonlocal ter-m θ(x)v(x0,t)where ODE represents the system execution and drive.We will use the Backstepping method to design the controller to prove the closed-loop system exponential stability.In the third chapter,we consider the vibration behavior of the Schrodinger equation with nonlocal terms μu(x0,t).We choose a target system with damping term at the boundary,and design a state feedback controller to make the original system equivalent to the target system by using the Backstepping method.De-signing an output feedback controller based on an infinite-dimensional observer,we choose the proper state space H,define the system operator,using the opera-tor semigroup theory we prove that the closed-loop system is exponentially stable.Finally,we present some numerical results to illustrate the effectiveness of the con-troller.Chapter four concludes this thesis and presents some research works in the future.