Noncollocated adaptive output regulation of a Schrödinger equation with unknown exosystem

In this paper, we consider the output regulation problem of a 1-d Schrödinger equation, where the output and control input are located at opposite boundaries and the disturbances are generated from an unknown finite-dimensional exosystem. We apply an adaptive observer to estimate all possible unknown frequencies of the exosystem. The following work is aiming at designing an error feedback control to achieve the output regulation and disturbances rejection based on the adaptive internal model. The closed-loop system is proved to be well-posed and bounded. The numerical simulations are carried out to demonstrate that the proposed controller is effective and the tracking error converges to zero.