Stabilization for an ensemble of half-spin systems
Contribuinte(s) |
UNIVERSIDADE DE SÃO PAULO |
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Data(s) |
24/10/2013
24/10/2013
2012
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Resumo |
Feedback stabilization of an ensemble of non interacting half spins described by the Bloch equations is considered. This system may be seen as an interesting example for infinite dimensional systems with continuous spectra. We propose an explicit feedback law that stabilizes asymptotically the system around a uniform state of spin +1/2 or -1/2. The proof of the convergence is done locally around the equilibrium in the H-1 topology. This local convergence is shown to be a weak asymptotic convergence for the H-1 topology and thus a strong convergence for the C 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 equilibrium. (C) 2011 Elsevier Ltd. All rights reserved. Agence Nationale de la Recherche (ANR) Agence Nationale de la Recherche (ANR) [BLAN-3-139579] CNPq Conselho Nacional de Desenvolvimento Cientifico e Tecnologico Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq) Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP), Brazil Fundacao do Amparo a Pesquisa do Estado de Sao Paulo FAPESP, Brazil |
Identificador |
AUTOMATICA, OXFORD, v. 48, n. 1, supl. 1, Part 3, pp. 68-76, JAN, 2012 0005-1098 http://www.producao.usp.br/handle/BDPI/35966 10.1016/j.automatica.2011.09.050 |
Idioma(s) |
eng |
Publicador |
PERGAMON-ELSEVIER SCIENCE LTD OXFORD |
Relação |
AUTOMATICA |
Direitos |
restrictedAccess Copyright PERGAMON-ELSEVIER SCIENCE LTD |
Palavras-Chave | #NONLINEAR SYSTEMS #LYAPUNOV STABILIZATION #LASALLE INVARIANCE #ENSEMBLE CONTROLLABILITY #INFINITE DIMENSIONAL SYSTEMS #BILINEAR SCHRODINGER-EQUATIONS #QUANTUM PARTICLE #POTENTIAL WELL #AUTOMATION & CONTROL SYSTEMS #ENGINEERING, ELECTRICAL & ELECTRONIC |
Tipo |
article original article publishedVersion |