Acta Applicandae Mathematicae

, Volume 135, Issue 1, pp 5–45 | Cite as

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

  • Bernard BonnardEmail author
  • Mathieu Claeys
  • Olivier Cots
  • Pierre Martinon


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.


Geometric optimal control Contrast imaging in NMR Direct method Shooting and continuation techniques Moment optimization 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Bernard Bonnard
    • 1
    • 2
    Email author
  • Mathieu Claeys
    • 3
    • 4
  • Olivier Cots
    • 2
  • Pierre Martinon
    • 5
  1. 1.Institut de Mathématiques de BourgogneUniversité de BourgogneDijonFrance
  2. 2.INRIA Sophia Antipolis MéditerranéeSophia AntipolisFrance
  3. 3.CNRSLAASToulouseFrance
  4. 4.Université de Toulouse, UPS, INSA, INP, ISAEUT1, UTM, LAASToulouseFrance
  5. 5.Inria and Ecole PolytechniquePalaiseauFrance

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