  Ground-based high contrast exoplanet imaging requires state-of-the-art
adaptive optics (AO) systems in order to detect extremely faint planets next to
their brighter host stars. For such extreme AO systems (with high actuator
count deformable mirrors over a small field of view), the lag time of the
correction (which can impact our system by the amount the wavefront has changed
by the time the system is able to apply the correction) which can be anywhere
from ~1-5 milliseconds, can cause wavefront errors on spatial scales that lead
to speckles at small angular separations from the central star in the final
science image. One avenue for correcting these aberrations is predictive
control, wherein previous wavefront information is used to predict the future
state of the wavefront in one-system-lag's time, and this predicted state is
applied as a correction with a deformable mirror. Here, we consider two methods
for predictive control: data-driven prediction using empirical orthogonal
functions and the physically-motivated predictive Fourier control. The
performance and robustness of these methods have not previously been compared
side-by-side. In this paper, we compare these predictors by applying them as
post-facto methods to simulated atmospheres and on-sky telemetry, to
investigate the circumstances in which their performance differs, including
testing them under different wind speeds, C_n^2 profiles, and time lags. We
also discuss future plans for testing both algorithms on the Santa Cruz Extreme
AO Laboratory (SEAL) testbed.
