Title :
Subriemannian geodesics and optimal control of spin systems
Author :
Khaneja, Navin ; Glaser, Steffen ; Brockett, Roger
Author_Institution :
Div. of Appl. Sci., Harvard Univ., Cambridge, MA, USA
Abstract :
Nuclear Magnetic Resonance (NMR) Spectroscopy in solution is an important modality for extracting structural information of macromolecules. In NMR spectroscopy, radio frequency electromagnetic pulses axe used to manipulate spin states of atomic nuclei. Pulse sequences that accomplish a desired spin control should be as short as possible in order to minimize the effects of thermal relaxation, and to optimize the sensitivity of the experiments. In this paper, we cast the problem of design of pulse sequences in NMR spectroscopy as a problem of time optimal control. It is shown that finding time optimal pulse sequences can be reduced to problems of computing subriemannian geodesics in certain homogeneous spaces. The use of geometric control techniques provides a systematic way of finding time optimal pulse sequences for transferring coherence and synthesizing unitary transformations in spin networks arising in coherent spectroscopy.
Keywords :
NMR spectroscopy; differential geometry; macromolecules; optimal control; homogeneous spaces; macromolecules; modality; nuclear magnetic resonance spectroscopy; optimal control; radio frequency electromagnetic pulses; spin systems; subriemannian geodesics; thermal relaxation; Atomic measurements; Control system synthesis; Data mining; EMP radiation effects; Geophysics computing; Network synthesis; Nuclear magnetic resonance; Optimal control; Radio frequency; Spectroscopy;
Conference_Titel :
American Control Conference, 2002. Proceedings of the 2002
Print_ISBN :
0-7803-7298-0
DOI :
10.1109/ACC.2002.1025214