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

Published online by Cambridge University Press:  20 June 2006

Andrei Agrachev  and
Thomas Chambrion
Andrei Agrachev
Affiliation:
SISSA, Via Beirouth 2-4, 34013 Trieste, Italy; agrachev@sissa.it
Thomas Chambrion
Affiliation:
SYSTeMS Group, University of Ghent, Technologiepark 914, 9052 Zwijnaarde, Belgium; Thomas.Chambrion@UGent.be
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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.

Keywords

Control systemssemi-simple Lie groupsRiemannian geometry.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 3 , July 2006 , pp. 409 - 441
Copyright
© EDP Sciences, SMAI, 2006

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