Geodesic
An estimation of the controllability time for single-input systems on compact Lie groups
ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 409-441

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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.

DOI : 10.1051/cocv:2006007
Classification : 22E46, 93B03
Keywords: control systems, semi-simple Lie groups, riemannian geometry 
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     title = {An estimation of the controllability time for single-input systems on compact {Lie} groups},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {409--441},
     publisher = {EDP-Sciences},
     volume = {12},
     number = {3},
     year = {2006},
     doi = {10.1051/cocv:2006007},
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     zbl = {1106.93006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2006007/}
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Agrachev, Andrei; Chambrion, Thomas. An estimation of the controllability time for single-input systems on compact Lie groups. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 409-441. doi: 10.1051/cocv:2006007

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