Adaptive regulator design for undamped second-order hyperbolic systems with output disturbances

In this paper, an adaptive regulator is designed for undamped second-order hyperbolic systems with output disturbances in the case where the input and output operators are collocated. The systems may have an infinite number of poles and zeros on the imaginary axis. The adaptive regulator is constructed by a high-gain adaptive feedback and a new type of the estimation mechanism for the unknown parameters of the disturbances. First, the well-posedness of the closed-loop system is justified. Next, the stability of the closed-loop system is analysed. An example is given to illustrate the theory.