Mario Sigalotti
Adiabatic control of the Schr\"odinger equation via conical intersections of the eigenvalues.
Wed, 02/16/2011 - 16:01 — SomNambulAuthors: Ugo Boscain, Mario Sigalotti, Paolo Mason, Francesca Chittaro
Subjects: Optimization and Control
AbstractIn this paper we present a constructive method to control the bilinear
Schr\"odinger equation via two controls. The method is based on adiabatic
techniques and works if the spectrum of the Hamiltonian admits eigenvalue
intersections, and if the latter are conical (as it happens generically). We
provide sharp estimates of the relation between the error and the
controllability time.Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces.
Thu, 06/10/2010 - 15:01 — SomNambulAuthors: Mario Sigalotti, Falk Hante
Subjects: Optimization and Control
AbstractWe consider switched systems on Banach and Hilbert spaces governed by
strongly continuous one-parameter semigroups of linear evolution operators. We
provide necessary and sufficient conditions for their global exponential
stability, uniform with respect to the switching signal, in terms of the
existence of a Lyapunov function common to all modes.Lipschitz classification of almost-Riemannian distances on compact oriented surfaces.
Fri, 03/26/2010 - 16:01 — SomNambulAuthors: Ugo Boscain, Grégoire Charlot, Roberta Ghezzi, Mario Sigalotti
Subjects: Optimization and Control
AbstractTwo-dimensional almost-Riemannian structures are generalized Riemannian
structures on surfaces for which a local orthonormal frame is given by a Lie
bracket generating pair of vector fields that can become collinear. We consider
the Carnot--Caratheodory distance canonically associated with an
almost-Riemannian structure and study the problem of Lipschitz equivalence
between two such distances on the same compact oriented surface.High order sufficient conditions for tracking.
Tue, 12/01/2009 - 16:01 — SomNambulAuthors: Mario Sigalotti, María Barbero-Liñán
Subjects: Optimization and Control
AbstractIn this paper, we study under which conditions the trajectories of a
mechanical control system can track any curve on the configuration manifold. We
focus on systems that can be represented as forced affine connection control
systems and we generalize the sufficient conditions for tracking known in the
literature. The sufficient conditions are expressed in terms of convex cones of
vector fields defined through particular brackets of the control vector fields
of the system. The tracking control laws obtained by our constructions depend
on several parameters.Generic controllability properties for the bilinear Schr\"odinger equation.
Tue, 12/01/2009 - 16:01 — SomNambulAuthors: Mario Sigalotti, Paolo Mason
Subjects: Optimization and Control
AbstractIn [15] we proposed a set of sufficient conditions for the approximate
controllability of a discrete-spectrum bilinear Schr\"odinger equation. These
conditions are expressed in terms of the controlled potential and of the
eigenpairs of the uncontrolled Schr\"odinger operator. The aim of this paper is
to show that these conditions are generic with respect to the uncontrolled and
the controlled potential, denoted respectively by $V$ and $W$.Two-Dimensional Almost-Riemannian Structures with Tangency Points.
Wed, 08/19/2009 - 19:30 — SomNambulAuthors: Andrei Agrachev, Ugo Boscain, Grégoire Charlot, Roberta Ghezzi, Mario Sigalotti
Subjects: Differential Geometry
AbstractTwo-dimensional almost-Riemannian structures are generalized Riemannian
structures on surfaces for which a local orthonormal frame is given by a Lie
bracket generating pair of vector ?elds that can become collinear. We study the
relation between the topological invariants of an almost-Riemannian structure
on a compact oriented surface and the rank-two vector bundle over the surface
which de?nes the structure. We analyse the generic case including the presence
of tangency points, i.e. points where two generators of the distribution and
their Lie bracket are linearly dependent.
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