Adaptive regulator design for a class of parabolic distributed parameter systems with disturbed outputs

In this paper an adaptive regulator is designed for collocated parabolic distributed parameter systems with disturbed outputs in the case of unbounded input and output operators. The adaptive regulator is constructed by the concept of high-gain output feedback and a new type of the estimation mechanism of the unknown parameters for the noise. The existence and uniqueness of the solution of the closed-loop system are justified. In the controlled system, the convergence of the system state to zero will be guaranteed.