**Abstract**: In this talk, we will review the machine learning technique of Dynamic Mode Decomposition (DMD) for continuous time systems and show how this may be extended to produce models for the state of an unknown control-affine systems using trajectory data. Trajectory data in this setting comes as a pair of control signals and the corresponding control trajectory. The DMD method for control-affine systems enables the prediction of the action of the system in response to a previously unobserved control signal. This will require a discussion of reproducing kernel Hilbert spaces (RKHSs), vector valued RKHSs, control Liouville operators, and multiplication operators.

**Speaker’s Bio**: Dr. Joel A. Rosenfeld is an Assistant Professor in the Department of Mathematics and Statistics at the University of South Florida and the Principal Investigator of the Learning Dynamics, Operators, and Controls with Kernels Group. His focus is on the study of operator theoretic machine learning techniques for unknown dynamical systems.

Dr. Rosenfeld is a Young Investigator Research Program awardee through the Air Force Office of Scientific Research, awarded in 2020.

He received his Ph.D. from the mathematics department at the University of Florida in 2013, under the advisement of Dr. Michael T. Jury, studying Operator Theory and Functional Analysis. Following graduate school, he was a postdoc in Mechanical Engineering at the University of Florida, under Dr. Warren E. Dixon, studying numerical methods in optimal control theory and fractional calculus. Subsequently, he joined the Department of Electrical Engineering and Computer Science at Vanderbilt University, under Dr. Taylor T. Johnson, studying numerical methods in formal methods for computing, which ultimately led to a position as a Senior Research Scientist Engineer within the Institute for Software Integrated Systems before accepting a position at the University of South Florida.

Last Updated: November 4, 2021 - 1:14 pm