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Section: New Results

Optimal control for quantum systems: the contrast problem in NMR

These studies aim at optimizing the contrast in Nuclear Magnetic Resonance imaging using advanced optimal control. As said in section 4.2 , our work on this problem is based on experiments conducted in Prof. S. Glaser in Munich, see [29] .

Theoretical aspects

Participants : Bernard Bonnard, John Marriott, Monique Chyba [University of Hawaii] , Gautier Picot [University of Hawaii] , Olivier Cots, Jean-Baptiste Caillau.

This is done in collaboration with University of Hawaii, and deals with many theoretical aspects of the contrast problem in NMR: analysis of the optimal flow [5] , feedback classification in relation with the relaxation times of the species [10] , [4] . John Marriott defended his PhD thesis on this topic, on August 28, 2013.

Numerical aspects

Participants : Bernard Bonnard, Jean-Baptiste Caillau, Olivier Cots, Mathieu Claeys [LAAS CNRS, Toulouse] , Pierre Martinon [COMMANDS team, Inria] .

We performed, in a collaboration with Pierre Martinon (COMMANDS team, Inria) and Mathieu Claeys (LAAS CNRS, Toulouse), a thorough comparison of the various available numerical methods in optimal control on this important physical problem. Direct and indirect methods (implemented in the Bocop and Hampath sofwares) were tested in the contrast problem, and LMI techniques were used to obtain global bounds on the extremum (in the contrast problem there are many local optima and the global optimality is a complicated issue). This successful collaboration is accounted for in [15] and was presented at the CDC conference [12]