TY - JOUR
T1 - Optimal control of inhomogeneous ensembles
AU - Ruths, Justin
AU - Li, Jr Shin
N1 - Funding Information:
Manuscript received February 15, 2011; revised July 16, 2011; accepted January 03, 2012. Date of publication April 26, 2012; date of current version July 19, 2012. This work was supported in part by the National Science Foundation (Career Award 0747877) and in part by the Air Force Office of Scientific Research (Young Investigator Award FA9550-10-1-0146). Recommended by Associate Editor P. Rouchon.
PY - 2012
Y1 - 2012
N2 - Inhomogeneity, in its many forms, appears frequently in practical physical systems. Readily apparent in quantum systems, inhomogeneity is caused by hardware imperfections, measurement inaccuracies, and environmental variations, and subsequently limits the performance and efficiency achievable in current experiments. In this paper, we provide a systematic methodology to mathematically characterize and optimally manipulate inhomogeneous ensembles with concepts taken from ensemble control. In particular, we develop a computational method to solve practical quantum pulse design problems cast as optimal ensemble control problems, based on multidimensional pseudospectral approximations. We motivate the utility of this method by designing pulses for both standard and novel applications. We also show the convergence of the pseudospectral method for optimal ensemble control. The concepts developed here are applicable beyond quantum control, such as to neuron systems, and furthermore to systems with by parameter uncertainty, which pervade all areas of science and engineering.
AB - Inhomogeneity, in its many forms, appears frequently in practical physical systems. Readily apparent in quantum systems, inhomogeneity is caused by hardware imperfections, measurement inaccuracies, and environmental variations, and subsequently limits the performance and efficiency achievable in current experiments. In this paper, we provide a systematic methodology to mathematically characterize and optimally manipulate inhomogeneous ensembles with concepts taken from ensemble control. In particular, we develop a computational method to solve practical quantum pulse design problems cast as optimal ensemble control problems, based on multidimensional pseudospectral approximations. We motivate the utility of this method by designing pulses for both standard and novel applications. We also show the convergence of the pseudospectral method for optimal ensemble control. The concepts developed here are applicable beyond quantum control, such as to neuron systems, and furthermore to systems with by parameter uncertainty, which pervade all areas of science and engineering.
KW - Convergence of numerical methods
KW - optimal control
KW - robust control
UR - http://www.scopus.com/inward/record.url?scp=84864749340&partnerID=8YFLogxK
U2 - 10.1109/TAC.2012.2195920
DO - 10.1109/TAC.2012.2195920
M3 - Article
AN - SCOPUS:84864749340
SN - 0018-9286
VL - 57
SP - 2021
EP - 2032
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 8
M1 - 6189046
ER -