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The motivation of this article is double. First of all we provide a geometrical framework to the application of the smooth continuation method in optimal control, where the concept of conjugate points is related to the convergence of the method. In particular, it can be applied to the analysis of the global optimality properties of the geodesic flows of a family of Riemannian metrics. Secondly, this study is used to complete the analysis of two-level dissipative quantum systems, where the system is depending upon three physical parameters, which can be used as homotopy parameters, and the time-minimizing trajectory for a prescribed couple of extremities can be analyzed by making a deformation of the Grushin metric on a two-sphere of revolution.
@article{COCV_2011__17_1_267_0,
author = {Bonnard, Bernard and Shcherbakova, Nataliya and Sugny, Dominique},
title = {The smooth continuation method in optimal control with an application to quantum systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {267--292},
publisher = {EDP-Sciences},
volume = {17},
number = {1},
year = {2011},
doi = {10.1051/cocv/2010004},
mrnumber = {2775196},
zbl = {1213.49027},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010004/}
}
TY - JOUR AU - Bonnard, Bernard AU - Shcherbakova, Nataliya AU - Sugny, Dominique TI - The smooth continuation method in optimal control with an application to quantum systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2011 SP - 267 EP - 292 VL - 17 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010004/ DO - 10.1051/cocv/2010004 LA - en ID - COCV_2011__17_1_267_0 ER -
%0 Journal Article %A Bonnard, Bernard %A Shcherbakova, Nataliya %A Sugny, Dominique %T The smooth continuation method in optimal control with an application to quantum systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 267-292 %V 17 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010004/ %R 10.1051/cocv/2010004 %G en %F COCV_2011__17_1_267_0
Bonnard, Bernard; Shcherbakova, Nataliya; Sugny, Dominique. The smooth continuation method in optimal control with an application to quantum systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 1, pp. 267-292. doi: 10.1051/cocv/2010004
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