  This paper presents a novel learning framework to construct Koopman
eigenfunctions for unknown, nonlinear dynamics using data gathered from
experiments. The learning framework can extract spectral information from the
full nonlinear dynamics by learning the eigenvalues and eigenfunctions of the
associated Koopman operator. We then exploit the learned Koopman eigenfunctions
to learn a lifted linear state-space model. To the best of our knowledge, our
method is the first to utilize Koopman eigenfunctions as lifting functions for
EDMD-based methods. We demonstrate the performance of the framework in state
prediction and closed loop trajectory tracking of a simulated cart pole system.
Our method is able to significantly improve the controller performance while
relying on linear control methods to do nonlinear control.
