BOUNDARY CONTROLLERS AND OBSERVERS FOR THE LINEARIZED SCHRODINGER EQUATION

doi:10.1137/070704290

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	BOUNDARY CONTROLLERS AND OBSERVERS FOR THE LINEARIZED SCHRODINGER EQUATION
	Krstic, Miroslav 1; Guo, Bao-Zhu2,3,4 ; Smyshlyaev, Andrey 1
	2011
发表期刊	SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN	0363-0129
卷号	49 期号:4 页码:1479-1497
摘要	We consider a problem of stabilization of the linearized Schrodinger equation using boundary actuation and measurements. We propose two different control designs. First, a simple proportional collocated boundary controller is shown to exponentially stabilize the system. However, the decay rate of the closed-loop system cannot be prescribed. The second, full-state feedback boundary control design, achieves an arbitrary decay rate. We formally view the Schrodinger equation as a heat equation in complex variables and apply the backstepping method recently developed for boundary control of reaction-advection-diffusion equations. The resulting controller is then supplied with the backstepping observer to obtain an output-feedback compensator. The designs are illustrated with simulations.
关键词	distributed parameter systems backstepping stabilization
DOI	10.1137/070704290
语种	英语
资助项目	National Natural Science Foundation of China ; National Basic Research Program of China[2011CB808002] ; National Research Foundation of South Africa
WOS研究方向	Automation & Control Systems ; Mathematics
WOS类目	Automation & Control Systems ; Mathematics, Applied
WOS记录号	WOS:000294309600006
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12188
专题	系统科学研究所
通讯作者	Krstic, Miroslav
作者单位	1.Univ Calif San Diego, Dept Mech & Aerosp Engn, La Jolla, CA 92093 USA 2.Acad Sinica, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Shanxi Univ, Sch Math Sci, Taiyuan 030006, Peoples R China 4.Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Wits, Johannesburg, South Africa
推荐引用方式 GB/T 7714	Krstic, Miroslav,Guo, Bao-Zhu,Smyshlyaev, Andrey. BOUNDARY CONTROLLERS AND OBSERVERS FOR THE LINEARIZED SCHRODINGER EQUATION[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION,2011,49(4):1479-1497.
APA	Krstic, Miroslav,Guo, Bao-Zhu,&Smyshlyaev, Andrey.(2011).BOUNDARY CONTROLLERS AND OBSERVERS FOR THE LINEARIZED SCHRODINGER EQUATION.SIAM JOURNAL ON CONTROL AND OPTIMIZATION,49(4),1479-1497.
MLA	Krstic, Miroslav,et al."BOUNDARY CONTROLLERS AND OBSERVERS FOR THE LINEARIZED SCHRODINGER EQUATION".SIAM JOURNAL ON CONTROL AND OPTIMIZATION 49.4(2011):1479-1497.