Stabilization of Ode-schrödinger Cascaded Systems Subject to Boundary Control Matched Disturbance

In this article, we consider the state feedback stabilization of ODESchrödinger cascaded systems with the external disturbance. We use the backstepping transformation to handle the unstable part of the ODE, then design a feedback control which is used to cope with the disturbance and stabilize the Schrödinger part. By active disturbance rejection control (ADRC) approach, the disturbance is estimated by a constant high gain estimator, then the feedback control law can be designed. Next, we show that the resulting closed-loop system is practical stable, where the peaking value appears in the initial stage and the stabilized result requires that the derivative of disturbance be uniformly bounded. To avoid the peak phenomenon and to relax the restriction on the disturbance, a time varying high gain estimator is presented and asymptotical stabilization of the corresponding closed-loop system is proved. Finally, the effectiveness of the proposed control is verified by numerical simulations.