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Optimal bilinear control of Gross-Pitaevskii equations
AuthorHintermüller, Michael In der Gemeinsamen Normdatei der DNB nachschlagen ; Marahrens, Daniel ; Markowich, Peter A. In der Gemeinsamen Normdatei der DNB nachschlagen ; Sparber, Christof
Published in
SIAM Journal on Control and Optimization, Philadelphia, Pa., 2013, Vol. 51, Issue 3, page 2509-2543
Publisher version
Document typeJournal Article
Keywords (EN)quantum control / bilinear optimal control problem / nonlinear Schrodinger equation / BoseEinstein condensate / Newtons method / MINRES algorithm / work induced by control
URNurn:nbn:at:at-ubg:3-714 Persistent Identifier (URN)
 The work is publicly available
Optimal bilinear control of Gross-Pitaevskii equations [0.46 mb]
Abstract (English)

A mathematical framework for optimal bilinear control of nonlinear Schrödingerequations of GrossPitaevskii type arising in the description of BoseEinstein condensates is presented.The obtained results generalize earlier efforts found in the literature in several aspects. Inparticular, the cost induced by the physical workload over the control process is taken into accountrather than the often used L2- or H1-norms for the cost of the control action. Well-posedness ofthe problem and existence of an optimal control are proved. In addition, the first order optimalitysystem is rigorously derived. Also a numerical solution method is proposed, which is based on aNewton-type iteration, and used to solve several coherent quantum control problems.