An estimation of the controllability time for single-input systems on compact Lie Groups

Andrei Agrachev; Thomas Chambrion

ESAIM: Control, Optimisation and Calculus of Variations (2006)

  • Volume: 12, Issue: 3, page 409-441
  • ISSN: 1292-8119

Abstract

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Geometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters of the flag manifolds; the latter are also explicitly computed in the paper.

How to cite

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Agrachev, Andrei, and Chambrion, Thomas. "An estimation of the controllability time for single-input systems on compact Lie Groups." ESAIM: Control, Optimisation and Calculus of Variations 12.3 (2006): 409-441. <http://eudml.org/doc/249680>.

@article{Agrachev2006,
abstract = { Geometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters of the flag manifolds; the latter are also explicitly computed in the paper. },
author = {Agrachev, Andrei, Chambrion, Thomas},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Control systems; semi-simple Lie groups; Riemannian geometry. ; Riemannian geometry},
language = {eng},
month = {6},
number = {3},
pages = {409-441},
publisher = {EDP Sciences},
title = {An estimation of the controllability time for single-input systems on compact Lie Groups},
url = {http://eudml.org/doc/249680},
volume = {12},
year = {2006},
}

TY - JOUR
AU - Agrachev, Andrei
AU - Chambrion, Thomas
TI - An estimation of the controllability time for single-input systems on compact Lie Groups
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2006/6//
PB - EDP Sciences
VL - 12
IS - 3
SP - 409
EP - 441
AB - Geometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters of the flag manifolds; the latter are also explicitly computed in the paper.
LA - eng
KW - Control systems; semi-simple Lie groups; Riemannian geometry. ; Riemannian geometry
UR - http://eudml.org/doc/249680
ER -

References

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