# 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

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topAgrachev, 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 -

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