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This article is aimed at extending the framework of optimal controltechniques to the situation where the control field values are restricted to afinite set. We propose a generalization of the standard GRAPE algorithm suitedto this constraint. We test the validity and the efficiency of this approachfor the inversion of an inhomogeneous ensemble of spin systems with differentoffset frequencies. It is shown that a remarkable efficiency can be achievedeven for a very limited number of discrete values. Some applications in NuclearMagnetic Resonance are discussed.

A discrete-pulse optimal control algorithm with an application to spin systems