Lab Home | Phone | Search
Center for Nonlinear Studies  Center for Nonlinear Studies
 Home 
 People 
 Current 
 Postdocs 
 Visitors 
 Students 
 Research 
 Publications 
 Conferences 
 Workshops 
 Sponsorship 
 Talks 
 Seminars 
 Postdoc Seminars Archive 
 Quantum Lunch 
 Quantum Lunch Archive 
 P/T Colloquia 
 Archive 
 Ulam Scholar 
 
 Postdoc Nominations 
 Students 
 Student Program 
 Visitors 
 Description 
 Past Visitors 
 Services 
 General 
 
 History of CNLS 
 
 Maps, Directions 
 CNLS Office 
 T-Division 
 LANL 
 
Tuesday, July 09, 2024
4:00 PM - 5:00 PM
CNLS Conference Room (TA-3, Bldg 1690)

Seminar

Koopman Operator Workshop Part III - Generalizations to Control Affine and Higher Order Dynamical Systems

Prof. Joel Rosenfeld
Department of Mathematics and Statistics, University of South Florida

We continue to exploit the structure of the algorithm presented in Part I of the talks and leverage the Liouville or Koopman generator framework that yields pointwise convergence to the system state to motivate further generalizations. In this talk we are going to explore vector valued reproducing kernel HIlbert spaces and how we can leverage them to define a new operator, the control Liouville operator, that allows us to learn the drift dynamics and control effectiveness for a nonlinear control affine dynamical system. Then through the incorporation of a new type of multiplication operator, we can make predictions of a known state feedback controller after several observations of other state control pairs.

The second half of this talk will examine a new kind of nonlocal operator designed to model higher order dynamical systems without the use of state augmentation. Higher order dynamics frequently employ state augmentation to convert them into first order dynamical systems, but this requires the inflation of the state dimension. From the machine learning perspective, this can make learning unknowns much more difficult by way of the curse of dimensionality. This new high order Liouville operator allows for the direct treatment of higher order dynamical systems, and employs a new notion of vector valued reproducing kernel HIlbert space called a signal valued reproducing kernel Hilbert space.

Host: Humberto C Godinez (CCS-2) and Nishant Panda (CCS-3)