Title: Periodic Pulsed Controllability with Applications to NMR
Description: In this thesis we study a class of problems that require simultaneously controlling a large number of dynamical systems with varying system dynamics using the same control signal. We call such problems, ensemble control problems as the goal is to simultaneously steer the entire ensemble of systems. These problems are motivated by many physical systems and we will be particularly interested in the manipulation of nuclear spins in Nuclear Magnetic Resonance (NMR) experiments. System dispersions arise from imprecise magnets for controls, or from disruptive intermolecular interactions. In all cases, the aim is to attenuate the aspects of the dynamics that correspond to noise or errors, while preserving the aspects that contain the quantities of interest. In liquid NMR experiments this could correspond to preserving Larmor frequency in the presence of inhomogeneities of the strength of the applied radio frequency (RF) field. In solid state NMR, reducing or eliminating orientation dependent magnetic fields is of key concern, so that a precise spectrum can be observed.