Semi-global weak stabilization of bilinear Schrodinger equations

被引：18

作者：

Beauchard, Karine ^{[1
]}

Nersesyan, Vahagn ^{[2
]}

机构：

[1] CNRS, CMLA ENS Cachan, F-94230 Cachan, France

[2] Lab Math Versailles, F-78035 Versailles, France

来源：

COMPTES RENDUS MATHEMATIQUE | 2010年 / 348卷 / 19-20期

关键词：

QUANTUM PARTICLE; LYAPUNOV CONTROL; POTENTIAL WELL; CONTROLLABILITY; SYSTEMS;

D O I：

10.1016/j.crma.2010.09.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a linear Schrodinger equation on a bounded domain with bilinear control representing a quantum particle in an electric field (the control) Recently Nersesyan proposed explicit feedback laws and proved the existence of a sequence of times (t(n))(n is an element of N) for which the values of the solution of the closed loop system converge weakly in H(2) to the ground state Here we prove the convergence of the whole solution as t -> +infinity The proof relies on control Lyapunov functions and an adaptation of the LaSalle invariance principle to PDEs (C) 2010 Academie des sciences Published by Elsevier Masson SAS All rights reserved

引用

页码：1073 / 1078

页数：6

共 16 条

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[2] FEEDBACK STABILIZATION OF DISTRIBUTED SEMI-LINEAR CONTROL-SYSTEMS [J].