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

Andrei AgrachevThomas Chambrion — 2006

ESAIM: Control, Optimisation and Calculus of Variations

Geometric control theory and Riemannian techniques are used to describe the reachable set at time 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...

Smooth optimal synthesis for infinite horizon variational problems

Andrei A. AgrachevFrancesca C. Chittaro — 2009

ESAIM: Control, Optimisation and Calculus of Variations

We study Hamiltonian systems which generate extremal flows of regular variational problems on smooth manifolds and demonstrate that negativity of the generalized curvature of such a system implies the existence of a global smooth optimal synthesis for the infinite horizon problem. We also show that in the Euclidean case negativity of the generalized curvature is a consequence of the convexity of the Lagrangian with respect to the pair of arguments. Finally, we give a generic classification for...

Sub-Riemannian Metrics: Minimality of Abnormal Geodesics versus Subanalyticity

Andrei A. AgrachevAndrei V. Sarychev — 2010

ESAIM: Control, Optimisation and Calculus of Variations

We study sub-Riemannian (Carnot-Caratheodory) metrics defined by noninvolutive distributions on real-analytic Riemannian manifolds. We establish a connection between regularity properties of these metrics and the lack of length minimizing abnormal geodesics. Utilizing the results of the previous study of abnormal length minimizers accomplished by the authors in [Annales IHP. , p. 635-690] we describe in this paper two classes of the germs of distributions (called 2-generating and medium fat) such...

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