Stabilization of an arbitrary profile for an ensemble of half-spin systems

Autor:	Beauchard, Karine, da Silva, Paulo Sergio Pereira, Rouchon, Pierre
Rok vydání:	2012
Předmět:	Mathematics - Optimization and Control
Druh dokumentu:	Working Paper
Popis:	We consider the feedback stabilization of a variable profile for an ensemble of non interacting half spins described by the Bloch equations. We propose an explicit feedback law that stabilizes asymptotically the system around a given arbitrary target profile. The convergence proof is done when the target profile is entirely in the south hemisphere or in the north hemisphere of the Bloch sphere. The convergence holds for initial conditions in a H^1 neighborhood of this target profile. This convergence is shown for the weak H^1 topology. The proof relies on an adaptation of the LaSalle invariance principle to infinite dimensional systems. Numerical simulations illustrate the efficiency of these feedback laws, even for initial conditions far from the target profile. Comment: 6 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1202.5407 Zobrazit plný text záznamu View this record from Arxiv