Stabilization for Schrödinger Equation with Internal Damping and Boundary Disturbance

In this paper, the stabilization for Schrödinger equation subject to internal damping and boundary disturbance at the control end is investigated. Due to its immeasurability, the nonlinear observer system is designed to obtain the state information, and the existence of weak solution and its convergence for the nonlinear observer system are proved. The feedback control is realized by the backstepping transformation. In addition, the adaptive disturbance rejection control is applied to estimate the disturbance. According to the observer and disturbance estimation, the feedback control is finally designed to stabilize the system asymptotically.