Electron. J. Diff. Equ., Vol. 2015 (2015), No. 248, pp. 1-22.

Stabilization of ODE-Schrodinger cascaded systems subject to boundary control matched disturbance

Ya-Ping Guo, Jun-Jun Liu

In this article, we consider the state feedback stabilization of ODE-Schrodinger 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 Schrodinger 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.

Submitted August 13, 2015. Published September 23, 2015.
Math Subject Classifications: 93C20.
Key Words: Cascade systems; disturbance; backstepping; boundary control; active disturbance rejection control.

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Ya-ping Guo
School of Mathematics and Statistics
Beijing Institute of Technology
Beijing 100081, China
email: guoyaping0904@163.com
Jun-Jun Liu
Department of Mathematics
Taiyuan university of technology
Taiyuan 030024, China
email: liujunjun@tyut.edu.cn

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