Dynamic Mode Decomposition with Control Liouville Operators

This manuscript provides a theoretical foundation for the Dynamic Mode Decomposition (DMD) of control affine dynamical systems through vector valued reproducing kernel Hilbert spaces (RKHSs). Specifically, Liouville operators and occupation kernels are introduced to separate drift dynamics from effectiveness components. Given known feedback controller that is represented multiplication operator, DMD analysis may be performed on composition these make predictions concerning system controlled by controller.