# The smooth continuation method in optimal control with an application to quantum systems

Bernard Bonnard; Nataliya Shcherbakova; Dominique Sugny

ESAIM: Control, Optimisation and Calculus of Variations (2011)

- Volume: 17, Issue: 1, page 267-292
- ISSN: 1292-8119

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topBonnard, Bernard, Shcherbakova, Nataliya, and Sugny, Dominique. "The smooth continuation method in optimal control with an application to quantum systems." ESAIM: Control, Optimisation and Calculus of Variations 17.1 (2011): 267-292. <http://eudml.org/doc/272928>.

@article{Bonnard2011,

abstract = {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.},

author = {Bonnard, Bernard, Shcherbakova, Nataliya, Sugny, Dominique},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {optimal control; smooth continuation method; quantum control},

language = {eng},

number = {1},

pages = {267-292},

publisher = {EDP-Sciences},

title = {The smooth continuation method in optimal control with an application to quantum systems},

url = {http://eudml.org/doc/272928},

volume = {17},

year = {2011},

}

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

PB - EDP-Sciences

VL - 17

IS - 1

SP - 267

EP - 292

AB - 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.

LA - eng

KW - optimal control; smooth continuation method; quantum control

UR - http://eudml.org/doc/272928

ER -

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