TY - JOUR
T1 - Constrained minimum-energy optimal control of the dissipative Bloch equations
AU - Stefanatos, Dionisis
AU - Li, Jr Shin
N1 - Funding Information:
This work was supported by the NSF under the Career Award #0747877 and the AFOSR Young Investigator Award #FA9550-10-1-0146. The authors would like to thank the anonymous referee for valuable comments and for bringing the recent paper [13] to our attention.
PY - 2010/10
Y1 - 2010/10
N2 - In this letter, we apply optimal control theory to design minimum-energy π2 and π pulses for the Bloch system in the presence of relaxation with constrained control amplitude. We consider a commonly encountered case in which the transverse relaxation rate is much larger than the longitudinal one so that the latter can be neglected. Using Pontryagin's maximum principle, we derive optimal feedback laws which are characterized by the number of switches, depending on the control bound and the coordinates of the desired final state.
AB - In this letter, we apply optimal control theory to design minimum-energy π2 and π pulses for the Bloch system in the presence of relaxation with constrained control amplitude. We consider a commonly encountered case in which the transverse relaxation rate is much larger than the longitudinal one so that the latter can be neglected. Using Pontryagin's maximum principle, we derive optimal feedback laws which are characterized by the number of switches, depending on the control bound and the coordinates of the desired final state.
KW - Bloch equations
KW - Maximum principle
UR - http://www.scopus.com/inward/record.url?scp=77957870283&partnerID=8YFLogxK
U2 - 10.1016/j.sysconle.2010.07.004
DO - 10.1016/j.sysconle.2010.07.004
M3 - Article
AN - SCOPUS:77957870283
SN - 0167-6911
VL - 59
SP - 601
EP - 607
JO - Systems and Control Letters
JF - Systems and Control Letters
IS - 10
ER -