Backstepping Control For Several Classes Of Coupled Distributed Parameter Systems

Coupled distributed parameter systems are often used to describe many phenomena in engineering practice,such as,chemical coupling reaction,population coupling and mechanical coupling,etc.Due to the interaction and relation of coupled subsystems,the coupled systems become more complicated,in addition,the coupled systems may be unstable due to the existence of external disturbances and delays.Therefore,it is theoretically challenging and practically valuable to study the related control problems of coupled distributed parameter systems.Based on backstepping method,this paper studies the control design and stabilization analysis for several classes of coupled distributed parameter systems.The first chapter introduces the research background and the development situation on backstepping control design of coupled distributed parameter systems.Then the main work and innovative points of this paper are briefly described.Finally,some related mathematical theories are given.In chapter 2,for the coupled wave systems with spatially-varying coefficients,a state feedback controller is designed,and the exponential stabilization of the closed-loop system is proved.When the coupled system is transformed into a stable target system,the hyperbolic equations satisfied by the kernel functions in the Volterra transformation are derived.A new variable substitution is proposed to convert the hyperbolic equations into the corresponding integral equations,it is proved that the integral equation has a unique solution by the method of successive approximations and then the existence and uniqueness of the kernel functions are obtained.Chapter 3 discusses the disturbance estimator design and the output feedback controller design for the wave-ODE coupled systems with the disturbance.Firstly,based on the new Active Disturbance Rejection Control(ADRC)method,a disturbance estimator is designed by constructing two appropriate infinite dimensional auxiliary systems.Then,an observer is designed by adding the injection of error between the measurable outputs and their observer values to the original coupled system.Finally,an output feedback controller is designed which uses the information from the disturbance estimator and the observer,and the exponential stabilization of the closed-loop system is proved.Chapter 4 considers the output feedback stabilization of the wave-ODE coupled system with the input and output delay.The output delay is transformed into a first-order hyperbolic equation,resulting in a wave-ODE-transport coupled system.For this coupled system,an output feedback controller is designed with only one measurable output,and the exponential stabilization of the closed-loop system is proved.In addition,when there exists an input delay mismatch,that is,there is an error between the exact input delay and the identified input delay,a new output feedback controller is designed.Moreover,the exponential stabilization of the closed-loop system with the input delay mismatch is also proved.The fifth chapter makes a brief summary for this work,and lists some problems to be further studied.