Lyapunov control of bilinear Schrodinger equations

被引:157
作者
Mirrahimi, M
Rouchon, P
Turinici, G
机构
[1] Ecole Mines, Ctr Automat & Syst, F-75272 Paris, France
[2] INRIA Rocquencourt, F-78153 Le Chesnay, France
[3] CERMICS ENPC, F-77455 Marne La Vallee, France
关键词
quantum systems; stabilization; control Lyapunov function; adiabatic invariant; tracking; trajectory generation;
D O I
10.1016/j.automatica.2005.05.018
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
A Lyapunov-based approach for trajectory tracking of the Schrodinger equation is proposed. In the finite dimensional case, convergence is precisely analyzed. Connection between the controllability of the linearized system around the reference trajectory and asymptotic tracking is studied. When the linearized system is controllable, such a feedback ensures almost global asymptotic convergence. When the linearized system is not controllable, the stability of the closed-loop system is not asymptotic. To overcome such lack of convergence, we propose, when the reference trajectory is an eigenstate, a modification based on adiabatic invariance. Simulations illustrate the simplicity and also the interest for trajectory generation. (c) 2005 Elsevier Ltd. All rights reserved.
引用
收藏
页码:1987 / 1994
页数:8
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