Optical and control setup used for simulations, described in Sect. 4. The wavefront is propagated through atmospheric turbulence, followed by a DM. The beam is then split, with half the light going to a WFS and the other half propagating through the APP coronagraph to the science camera. A phase aberration is added to the latter beam to simulate NCPA. The DM is controlled using a nonlinear control system as described in Radhakrishnan et al. (2018) to maximize focal-plane contrast rather than flatten the wavefront. The controller is driven based on inputs from the WFS as well as information from the focal plane.