Ensemble Control Synthesis via the Singular Value Decomposition
Anatoly Zlotnik (Washington University)
SYSTEMS AND CONTROL SERIESDATE: 2012-06-22
TIME: 11:00:00 - 12:00:00
LOCATION: RSISE Seminar Room, ground floor, building 115, cnr. North and Daley Roads, ANU
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ABSTRACT:
An emerging and challenging area in mathematical control theory called Ensemble Control encompasses a class of problems that involves the guidance of an uncountably infinite collection of structurally identical dynamical systems, which are indexed by a parameter set, by applying a common open-loop control. The subject originates from the study of complex spin dynamics in Nuclear Magnetic Resonance (NMR) spectroscopy and imaging (MRI). For ensembles of finite-dimensional time-varying linear systems, the necessary and sufficient controllability conditions and analytical optimal control laws have been recently established. I will describe a computationally efficient algorithm based on the singular value decomposition (SVD) that approximates ensemble controls of minimum norm for such systems. Extension of this method to synthesize controls for certain classes of bilinear systems will be discussed, as well as optimal frequency control of oscillator ensembles.
BIO:
Anatoly Zlotnik is a PhD candidate in Systems Science and Mathematics at Washington University in Saint Louis, Missouri working at the interface between control, optimization, and computation. He is visiting the ANU as a fellow of the East Asia and Pacific Summer Institutes (EAPSI), a program supported by the United States National Science Foundation and the Australian Academy of Science. He holds an MS degree in Applied Mathematics from the University of Nebraska - Lincoln, as well as BSE and MSE degrees in Systems and Control Engineering from Case Western Reserve University in Cleveland, Ohio.
