Generic controllability properties for the bilinear Schrödinger equation

Author

Sigalotti, Mario ; Mason, Paolo ; Boscain, Ugo ; Chambrion, Thomas

Author_Institution

INRIA Nancy - Grand Est, Nancy Univ., Vandoeuvre-les-Nancy, France

fYear

2009

fDate

15-18 Dec. 2009

Firstpage

3799

Lastpage

3804

Abstract

In a recent paper we proposed a set of sufficient conditions for the approximate controllability of a discrete-spectrum bilinear Schrodinger equation on a fixed domain. These conditions are expressed in terms of the controlled potential and of the eigenpairs of the uncontrolled Schrodinger operator. The aim of this presentation is to show that these conditions are generic with respect to the uncontrolled or the controlled potential. The results are obtained by analytic perturbation arguments and through the study of asymptotic properties of eigenfunctions.

Keywords

Schrodinger equation; controllability; discrete systems; eigenvalues and eigenfunctions; perturbation techniques; analytic perturbation arguments; approximate controllability; asymptotic properties; discrete-spectrum bilinear Schrodinger equation; eigenfunctions; eigenpairs; fixed domain; generic controllability properties; sufficient conditions; uncontrolled Schrodinger operator; Control systems; Controllability; Differential equations; Eigenvalues and eigenfunctions; Robust control; Sufficient conditions; Wave functions;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on

Conference_Location

Shanghai

ISSN

0191-2216

Print_ISBN

978-1-4244-3871-6

Electronic_ISBN

0191-2216

Type

conf

DOI

10.1109/CDC.2009.5399813

Filename

5399813