Adaptive servomechanism design for boundary control systems

In this paper we consider the design of adaptive servomechanism for boundary control systems in the case of the input and output operators being collocated. An adaptive servomechanism is constructed by the concept of high‐gain output feedback and the estimation mechanism of the unknown parameters for the bounded disturbances. Moreover, a controller is designed to be inverse optimal. It minimizes a meaningful cost functional that incorporates integral penalty on the tracking error state, the control and the parameter error.