Geometric and Numerical Methods in the Contrast Imaging Problem in Nuclear Magnetic Resonance

被引：15
作者：
Bonnard, Bernard [1 ,2 ]
Claeys, Mathieu [3 ,4 ]
Cots, Olivier [2 ]
Martinon, Pierre [5 ,6 ]
机构：
[1] Univ Bourgogne, Inst Math Bourgogne, F-21078 Dijon, France
[2] INRIA Sophia Antipolis Mediterranee, F-06902 Sophia Antipolis, France
[3] CNRS, LAAS, F-31077 Toulouse, France
[4] Univ Toulouse, UPS, INSA, INP,ISAE,UT1,UTM,LAAS, F-31077 Toulouse, France
[5] Inria, F-91128 Palaiseau, France
[6] Ecole Polytech, F-91128 Palaiseau, France
来源：
ACTA APPLICANDAE MATHEMATICAE | 2015年 / 135卷 / 01期
关键词：
Geometric optimal control; Contrast imaging in NMR; Direct method; Shooting and continuation techniques; Moment optimization; ALGORITHM;
D O I：
10.1007/s10440-014-9947-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, the contrast imaging problem in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. The optimal solution can be found as an extremal, solution of the Maximum Principle and analyzed with the techniques of geometric control. This leads to a numerical investigation based on so-called indirect methods using the HamPath software. The results are then compared with a direct method implemented within the Bocop toolbox. Finally lmi techniques are used to estimate a global optimum.
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页码：5 / 45
页数：41
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