  High-order wavefront sensing and control (HOWFSC) is key to create a dark
hole region within the coronagraphic image plane where high contrasts are
achieved. The Roman Coronagraph is expected to perform its HOWFSC with a
ground-in-the-loop scheme due to the computational complexity of the Electric
Field Conjugation (EFC) algorithm. This scheme provides the flexibility to
alter the HOWFSC algorithm for given science objectives. The baseline HOWFSC
scheme involves running EFC while observing a bright star such as {\zeta}
Puppis to create the initial dark hole followed by a slew to the science
target. The new implicit EFC (iEFC) algorithm removes the optical diffraction
model from the controller, making the final contrast independent of model
accuracy. While previously demonstrated with a single DM, iEFC is extended to
two deformable mirror systems in order to create annular dark holes. The
algorithm is then applied to the Wide-Field-of-View Shaped Pupil Coronagraph
(SPC-WFOV) mode designed for the Roman Space Telescope using end-to-end
physical optics models. Initial monochromatic simulations demonstrate the
efficacy of iEFC as well as the optimal choice of modes for the SPC-WFOV
instrument. Further simulations with a 3.6% wavefront control bandpass and a
broader 10% bandpass then demonstrate that iEFC can be used in broadband
scenarios to achieve contrasts below 1E-8 with Roman. Finally, an EMCCD model
is implemented to estimate calibration times and predict the controller's
performance. Here, 1E-8 contrasts are achieved with a calibration time of about
6.8 hours assuming the reference star is {\zeta} Puppis. The results here
indicate that iEFC can be a valid HOWFSC method that can mitigate the risk of
model errors associated with space-borne coronagraphs, but to maximize iEFC
performance, lengthy calibration times will be required to mitigate the noise
accumulated during calibration.
