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- Ugo V. Boscain, Marco Caponigro, Thomas Chambrion, Mario Sigalotti
- ArXiv
- 2011

In this paper we prove an approximate controllability result for the bilinear Schrödinger equation. This result requires less restrictive non-resonance hypotheses on the spectrum of the uncontrolled Schrödinger operator than those present in the literature. The control operator is not required to be bounded and we are able to extend the controllability… (More)

Given a compact manifold M , we prove that any bracket generating family of vector fields on M , which is invariant under multiplication by smooth functions, generates the connected component of the identity of the group of diffeomorphisms of M . Résumé Soit M une variété compacte, nous montrons que toute famille de champs de vecteurs satisfaisant la… (More)

Starting with the seminal papers of Reynolds (1987), Vicsek et. al. (1995) Cucker-Smale (2007), there has been a flood of recent works on models of self-alignment and consensus dynamics. Selforganization has been so far the main driving concept of this research direction. However, the evidence that in practice self-organization does not necessarily occur… (More)

- Nabile Boussaid, Marco Caponigro, Thomas Chambrion
- IEEE Trans. Automat. Contr.
- 2013

Weakly-coupled systems are a class of infinite dimensional conservative bilinear control systems with discrete spectrum. A property of these systems is that they can be precisely approached by finite dimensional Galerkin approximations. This feature is of particular interest for the approximation of quantum system dynamics and the control of the bilinear… (More)

We present a sufficient condition for approximate controllability of the bilinear discretespectrum Schrödinger equation exploiting the use of several controls. The controllability result extends to simultaneous controllability, approximate controllability in Hs, and tracking in modulus. The result is more general than those present in the literature even in… (More)

This article is mainly based on the work [7], and it is dedicated to the 60th anniversary of B. Bonnard, held in Dijon in June 2012. We focus on a controlled Cucker–Smale model in finite dimension. Such dynamics model self-organization and consensus emergence in a group of agents. We explore how it is possible to control this model in order to enforce or… (More)

We provide bounds on the error between dynamics of an infinite dimensional bilinear Schrödinger equation and of its finite dimensional Galerkin approximations. Standard averaging methods are used on the finite dimensional approximations to obtain constructive controllability results. As an illustration, the methods are applied on a model of a 2D rotating… (More)

This note presents an example of bilinear conservative system in an infinite dimensional Hilbert space for which approximate controllability in the Hilbert unit sphere holds for arbitrary small times. This situation is in contrast with the finite dimensional case and is due to the unboundedness of the drift operator.

- Alfio Borzí, Marco Caponigro
- Physics of life reviews
- 2016

- Nabile Boussäıd, Marco Caponigro, Thomas Chambrion
- 2013

This paper presents an energy estimate in terms of the total variation of the control for bilinear infinite dimensional quantum systems with unbounded potentials. These estimates allow a rigorous construction of propagators associated with controls of bounded variation. Moreover, upper bounds of the error made when replacing the infinite dimensional system… (More)