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Center for Nonlinear Studies |
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)