Monday, February 13, 2012

1202.2306 (Michael Hintermüller et al.)

Optimal bilinear control of Gross-Pitaevskii equations    [PDF]

Michael Hintermüller, Daniel Marahrens, Peter A. Markowich, Christof Sparber
A mathematical framework for optimal bilinear control of nonlinear
Schr\"odinger equations of Gross-Pitaevskii type arising in the description of
Bose-Einstein condensates is presented. The obtained results generalize earlier
efforts found in the literature in several aspects. In particular, the cost
induced by the physical work load over the control process is taken into
account rather then often used $L^2$- or $H^1$-norms for the cost of the
control action. Well-posedness of the problem and existence of an optimal
control is proven. In addition, the first order optimality system is rigorously
derived. Also a numerical solution method is proposed, which is based on a
Newton type iteration, and used to solve several coherent quantum control
problems.
View original: http://arxiv.org/abs/1202.2306

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