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

Agrachev, Andrei; Chambrion, Thomas

ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 409-441.

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.

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