| This paper studies the state feedback stabilization and output regulation problem of a class of wave equations with disturbances.Similar to the internal model principle,the disturbances generated by finite-dimensional systems are mainly considered.It is mainly introduced from the following two aspects.For the wave equation with disturbance in the control channel,if the disturbance is written as the output of the finite-dimensional system,we can regard the wave equation(PDE)as the execution dynamics of the external disturbance(ODE),and it can be transformed into a wave equation with PDE implements the stability problem of the dynamic ODE system.This chapter introduce the appropriate transformation,thus easier to design the controller,finally by semigroup method the stability of the whole system is proved.For the output regulation problem of wave equation with disturbance in all channels,the state feedback controller is designed first when the states are known,and then the appropriate transformation is introduced to eliminate the disturbance,which proves the stability of the new system and achieves exponential convergence of tracking errors.Then,the observer is designed by using the output and tracking errors,and the stability of the error system is proved.Finally,a controller based on output feedback is designed to prove the stability of the cascade system and achieve exponential convergence of tracking errors.In the first part of this paper,the kernel function of the controller design can be described by ordinary differential equation,the controller design is more simple and easy to understand,and the semigroup method is used to prove the stability of the system,avoiding the difficulty of the function construction of the Lyapunov method.In the second part of this paper,the method of fixed coefficient is not adopted,so it is more applicable to a wide range of problems.After adopting a transformation,all channels of the system have no disturbance,avoiding a lot of calculation.The output and tracking errors are used in observer design to make full use of known information. |
