Launch costs for high-resolution space telescopes for Earth observation can be reduced when the telescope mirrors are made deployable. However, such a system is subject to optical aberrations that decreases image quality. To counter these aberrations, an Aberration Correction System (ACS) is proposed that uses a deformable mirror (DM) which is calibrated by applying image sharpness optimisation. A stochastic gradient descent algorithm is applied to the output of two image detectors, such that the DM deformation can even be optimised during in-orbit scanning operations, without the need for a dedicated wavefront sensor. The effects of different sharpness metrics and algorithm settings have been analysed. With this novel control method, an average Strehl ratio of above 0.9 and 0.8 can be achieved on the central field and extreme field of the primary detector respectively. Also, in-orbit drift effects can be actively compensated without interrupting nominal operations.