International Journal of Robust and Nonlinear Control

Volume 24, Issue 16 pp. 2194-2212

Research Article

Sliding mode control and active disturbance rejection control to the stabilization of one-dimensional Schrödinger equation subject to boundary control matched disturbance

Bao-Zhu Guo,

Corresponding Author

Bao-Zhu Guo

Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100190, China

School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa

Correspondence to: Bao-Zhu Guo, Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100190, China.

E-mail: [email protected]

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Jun-Jun Liu,

Jun-Jun Liu

School of Mathematical Sciences, Beijing Institute of Technology, Beijing 100081, China

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Bao-Zhu Guo,

Corresponding Author

Bao-Zhu Guo

Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100190, China

School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa

Correspondence to: Bao-Zhu Guo, Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100190, China.

E-mail: [email protected]

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Jun-Jun Liu,

Jun-Jun Liu

School of Mathematical Sciences, Beijing Institute of Technology, Beijing 100081, China

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First published: 04 March 2013

https://doi.org/10.1002/rnc.2977

Citations: 111

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SUMMARY

In this paper, we are concerned with the boundary stabilization of a one-dimensional anti-stable Schrödinger equation subject to boundary control matched disturbance. We apply both the sliding mode control (SMC) and the active disturbance rejection control (ADRC) to deal with the disturbance. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed-loop system is proved and the ‘reaching condition’ is obtained. Considering the SMC usually requires the large control gain and may exhibit chattering behavior, we develop the ADRC to attenuate the disturbance for which the derivative is also supposed to be bounded. Compared with the SMC, the advantage of the ADRC is not only using the continuous control but also giving an online estimation of the disturbance. It is shown that the resulting closed-loop system can reach any arbitrary given vicinity of zero as time goes to infinity and high gain tuning parameter goes to zero. Copyright © 2013 John Wiley & Sons, Ltd.

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Volume24, Issue16

10 November 2014

Pages 2194-2212

Sliding mode control and active disturbance rejection control to the stabilization of one-dimensional Schrödinger equation subject to boundary control matched disturbance

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Sliding mode control and active disturbance rejection control to the stabilization of one-dimensional Schrödinger equation subject to boundary control matched disturbance

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