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
TypeCommunication / Conférence
External document linkhttp://hal.archives-ouvertes.fr/hal-00578331/fr/
Conference title50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC)
Book titleProceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 2011
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Abstract (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.
Subjects / KeywordsQuantum systems; Lyapunov trajectory; Schrodinger equations
Showing items related by title and author.
Coron, Jean-Luc; Grigoriu, Andreea; Lefter, Catalin; Turinici, Gabriel (2009) Article accepté pour publication ou publié