Stabilization Of Two Kinds Of ODE-heat Cascaded Systems With Nonlocal Terms

The control problem of nonlocal systems is a hot topic in recent years.This thesis mainly studies the stabilizability of the ODE-heat cascade system with memory and the nonlinear ODE-heat intermediate cascade system.The feedback controllers are designed by using the Backstepping method,and then the exponential stability of the closed-loop system is given by combining with the appropriate Lyapunov function.The first chapter mainly introduces the research background and the present situation,the question proposed as well as the related preliminary knowledge.In the second chapter,we mainly study the stabilizability of a class of ODEheat cascade systems with memory.A two-step Backstepping method is proposed to obtain the feedback control law by selecting the appropriate intermediate control system.The stability of the closed-loop system is proved by using the Lyapunov function and the boundedness of the reversible Backstepping transformation.Finally,the simulation results show the effectiveness of the controller design.In the third chapter,the stabilizability of a class of nonlinear ODE-heat intermediate cascade system is studied.By using Backstepping method,the original system is transformed into an exponentially stable target system by choosing appropriate parametric transformation,and the feedback control law is designed.In the process of solving the kernel,some mathematical techniques are used to verify the correctness of the consistency condition.Finally,through the exponential stability of the target system and the boundedness of the transformation,the exponential stability of the original system under the control law is obtained by using Lyapunov method.