Implicit Lyapunov control for Schrödinger equations with dipole and polarizability term
Grigoriu, Andreea (2011), Implicit Lyapunov control for Schrödinger equations with dipole and polarizability term, Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 2011, IEEE, p. 7362-7367
Type
Communication / ConférenceLien vers un document non conservé dans cette base
http://hal.archives-ouvertes.fr/hal-00578331/fr/Date
2011Titre du colloque
50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC)Date du colloque
2011-12Ville du colloque
OrlandoPays du colloque
Etats-UnisTitre de l'ouvrage
Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 2011Éditeur
IEEE
Isbn
978-1-61284-800-6
Pages
7362-7367
Métadonnées
Afficher la notice complèteAuteur(s)
Grigoriu, AndreeaRésumé (EN)
We analyze in this paper finite dimensional closed quantum systems in interaction with a laser field. The characteristic of the problem is that the interaction laser-system is modeled by a first order term (dipole coupling) and a second order term (polarisability coupling), that appear in the Hamiltonian of the Schrödinger equation. In order to determine the control, an implicit Lyapunov trajectory tracking procedure is applied when there is no direct coupling between the target state and the eigenvectors of the internal hamiltonian. The same type of algorithm is applied for the difficult case of degenerate systems too. The controlled Lyapunov function is defined by an implicit equation and its existence is shown by a fix point theorem. The convergence is analysed using the LaSalle invariance principle. The performance of the feedbacks is illustrated by numerical simulations.Mots-clés
Quantum systems; Lyapunov trajectory; Schrodinger equationsPublications associées
Affichage des éléments liés par titre et auteur.
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Coron, Jean-Luc; Grigoriu, Andreea; Lefter, Catalin; Turinici, Gabriel (2009) Article accepté pour publication ou publié
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Grigoriu, Andreea; Lefter, Catalin; Turinici, Gabriel (2009) Communication / Conférence
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Grigoriu, Andreea; Lefter, Catalin; Turinici, Gabriel (2009) Communication / Conférence
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Stability analysis of discontinous quantum control systems with dipole and polarizability coupling Grigoriu, Andreea (2012) Article accepté pour publication ou publié
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Turinici, Gabriel; Rouchon, Pierre; Mirrahimi, Mazyar (2005) Article accepté pour publication ou publié