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

¹ SISSA, Via Beirouth 2-4, 34013 Trieste, Italy; agrachev@sissa.it
² SYSTeMS Group, University of Ghent, Technologiepark 914, 9052 Zwijnaarde, Belgium; Thomas.Chambrion@UGent.be

Received: 4 September 2004
Revised: 8 May 2005

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.