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

被引:101
作者
Guo, Bao-Zhu [1 ,2 ]
Liu, Jun-Jun [3 ]
机构
[1] Acad Sinica, Acad Math & Syst Sci, Beijing 100190, Peoples R China
[2] Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa
[3] Beijing Inst Technol, Sch Math Sci, Beijing 100081, Peoples R China
基金
中国国家自然科学基金; 新加坡国家研究基金会;
关键词
Schrodinger equation; sliding mode control; active disturbance rejection control; stability; boundary control; disturbance rejection; UNCERTAIN HEAT;
D O I
10.1002/rnc.2977
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In this paper, we are concerned with the boundary stabilization of a one-dimensional anti-stable Schrodinger 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 (c) 2013 John Wiley & Sons, Ltd.
引用
收藏
页码:2194 / 2212
页数:19
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