Asymptotic ensemble stabilizability of the Bloch equation

Abstract : In this paper we are concerned with the stabilizability to an equilibrium point of an ensemble of non interacting half-spins. We assume that the spins are immersed in a static magnetic field, with dispersion in the Larmor frequency, and are controlled by a time varying transverse field. Our goal is to steer the whole ensemble to the uniform " down " position. Two cases are addressed: for a finite ensemble of spins, we provide a control function (in feedback form) that asymptotically stabilizes the ensemble in the " down " position, generically with respect to the initial condition. For an ensemble containing a countable number of spins, we construct a sequence of control functions such that the sequence of the corresponding solutions pointwise converges, asymptotically in time, to the target state, generically with respect to the initial conditions. The control functions proposed are uniformly bounded and continuous.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01504321
Contributeur : Francesca Carlotta Chittaro <>
Soumis le : lundi 10 avril 2017 - 11:52:29
Dernière modification le : mardi 11 avril 2017 - 01:07:09
Document(s) archivé(s) le : mardi 11 juillet 2017 - 12:13:21

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ensemble-ctr.pdf
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  • HAL Id : hal-01504321, version 1
  • ARXIV : 1704.02822

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Francesca Chittaro, Jean-Paul Gauthier. Asymptotic ensemble stabilizability of the Bloch equation. 2017. <hal-01504321>

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