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.
An estimation of the controllability time for single-input systems on compact groups / Agrachev, Andrey; Chambrion, T.. - In: ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. - ISSN 1262-3377. - 12:3(2006), pp. 409-441. [10.1051/cocv:2006007]
An estimation of the controllability time for single-input systems on compact groups
Agrachev, Andrey;
2006-01-01
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.File | Dimensione | Formato | |
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