The stability of Schrodinger equation with boundary control matched disturbance

被引：1

作者：

Zhang, Xiaoying ^{[1
,2
]}

Chai, Shugen ^{[1
]}

机构：

[1] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Peoples R China

[2] Shanxi Agr Univ, Dept Math, Taigu 030800, Peoples R China

来源：

JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY | 2017年 / 30卷 / 06期

关键词：

Active disturbance rejection control; extended state observer; Schrodinger equation; stability; OUTPUT-FEEDBACK STABILIZATION; UNSTABLE WAVE-EQUATION; ACTIVE DISTURBANCE; REJECTION CONTROL; SUBJECT;

D O I：

10.1007/s11424-017-6048-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper studies the stability of Schrodinger equation with boundary control matched disturbance. The time-varying gain extended state observer is utilized to estimate disturbance and state. Meanwhile, the authors get a continuous controller by the active disturbance rejection control strategy, which shows that the closed-loop system of Schrodinger equation is asymptotically stable. These results are illustrated by simulation examples.

引用

页码：1258 / 1269

页数：12

共 20 条

[11] Parameter Estimation and Non-Collocated Adaptive Stabilization for a Wave Equation Subject to General Boundary Harmonic Disturbance [J].

Guo, Wei ;

Guo, Bao-Zhu .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2013, 58 (07) :1631-1643

[12] Stabilization and regulator design for a one-dimensional unstable wave equation with input harmonic disturbance [J].

Guo, Wei ;

Guo, Bao-Zhu .

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2013, 23 (05) :514-533

[13] From PID to Active Disturbance Rejection Control [J].

Han, Jingqing .

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, 2009, 56 (03) :900-906

[14]

Komornik V., 2005, Fourier series in control theory

[15] BOUNDARY CONTROLLERS AND OBSERVERS FOR THE LINEARIZED SCHRODINGER EQUATION [J].

Krstic, Miroslav ;

Guo, Bao-Zhu ;

Smyshlyaev, Andrey .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2011, 49 (04) :1479-1497

[16]

Machtyngier E., 1994, Portugaliae Math-ematica, V51, P243

[17]

Tucsnak M, 2009, BIRKHAUSER ADV TEXTS, P1

[18] ADMISSIBILITY OF UNBOUNDED CONTROL OPERATORS [J].

WEISS, G .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1989, 27 (03) :527-545

[19] ADMISSIBLE OBSERVATION OPERATORS FOR LINEAR-SEMIGROUPS [J].

WEISS, G .

ISRAEL JOURNAL OF MATHEMATICS, 1989, 65 (01) :17-43

[20] On active disturbance rejection control for nonlinear systems using time-varying gain [J].

Zhao, Zhi-Liang ;

Guo, Bao-Zhu .

EUROPEAN JOURNAL OF CONTROL, 2015, 23 :62-70

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