 |
 |
Article dans une revue
Approximate stabilization of an infinite dimensional quantum stochastic system
Abstract : We study the state feedback stabilization of a quantum harmonic oscillator near a pre-specified Fock state (photon number state). Such a state feedback controller has been recently implemented on a quantized electromagnetic field in an almost lossless cavity. Such open quantum systems are governed by a controlled discrete-time Markov chain in the unit ball of an infinite dimensional Hilbert space. The control design is based on an unbounded Lyapunov function that is minimized at each time-step by feedback. This ensures (weak-*) convergence of probability measures to a final measure concentrated on the target Fock state with a pre-specified probability. This probability may be made arbitrarily close to 1 by choosing the feedback parameters and the Lyapunov function. They are chosen so that the stochastic flow that describes the Markov process may be shown to be tight (concentrated on a compact set with probability arbitrarily close to 1). Convergence proof uses Prohorov's theorem and specific properties of this Lyapunov function.
Littérature citée [13 références]
https://hal-mines-paristech.archives-ouvertes.fr/hal-00829864
Contributeur : François Chaplais <>
Soumis le : mardi 4 juin 2013 - 06:30:39
Dernière modification le : jeudi 24 septembre 2020 - 17:04:18
Archivage à long terme le : : jeudi 5 septembre 2013 - 04:20:11
Contributeur : François Chaplais <>
Soumis le : mardi 4 juin 2013 - 06:30:39
Dernière modification le : jeudi 24 septembre 2020 - 17:04:18
Archivage à long terme le : : jeudi 5 septembre 2013 - 04:20:11
Fichier
StabilizationQuantum.pdf
Fichiers produits par l'(les) auteur(s)