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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.

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, feedback classification in relation with the relaxation times of the species. This activity has been the object of two publications [5] , [4] , and a conference talk [14] on feedback classification in the contrast problem, that will be followed by a journal article.

John Marriott will defend his Phd thesis on this topic, august 28, 2013; This will be followed by a two day conference on quantum control systems with applications, supported by a NSF grant and by the Engineering Department (P.E. Crouch).

Experimental aspects

Participants : Bernard Bonnard, Olivier Cots, Dominique Sugny [Univ. de Bourgogne] , Steffan Glaser [TU München] .

As said in section 4.2 , our work on this problem is based on experiments conducted in Prof. S. Glaser in Munich. Experiments using our techniques and measuring the improvement between materials that have an importance in medicine, like oxygenated and de-oxygenated blood have been conducted successfully, see [7] , [9] .

Numerical aspects

Participants : Bernard Bonnard, Olivier Cots, Jean-Baptiste Caillau.

In december, Pierre Martinon and Mathieu Caeys visited our group. This launhes a collaboration whose objective is to compare the direct and indirect methods in the contrast problem (implemented in the Bocop and Hampath sofwares) and use LMI techniques to get a global bound on the problem (in the contrast problem there are many local optima and the global optimality is a complicated issue)-also O. Cots visited R. Zidani (COMMANDS team) to investigate the use of numerical HJB techniques in the problem. This collaboration will allow to compare in a physical important problem the various available numerical methods in optimal control.