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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
Author(s) -
Guo BaoZhu,
Liu JunJun
Publication year - 2013
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.2977
Subject(s) - disturbance (geology) , control theory (sociology) , bounded function , boundary (topology) , active disturbance rejection control , sliding mode control , uniqueness , mode (computer interface) , mathematics , control (management) , computer science , nonlinear system , physics , mathematical analysis , state observer , paleontology , quantum mechanics , artificial intelligence , operating system , biology
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.