An adaptive optics system with a single deformable mirror is being implemented on the THEMIS 90cm solar telescope. This system is designed to operate in the visible and is required to be as robust as possible in order to deliver the best possible correction in any atmospheric conditions, even if wavefronts are sensed on some low-contrast solar granulation. In extreme conditions, the images given by the subapertures of the Shack-Hartmann wavefront sensor get randomly blurred in space, in the set of subapertures, and the distribution of blurred images is rapidly changing in time, some of them possibly fading away. The algorithms we have developed for such harsh conditions rely on inverse problem approach. As an example, with the gradients of the wavefronts, the wavefront sensor also estimates their errors, including their covariance. This information allows the control loop to promptly optimize itself to the fast varying conditions, both in space (wavefront reconstruction) and in time. A major constraint is to fit the calculations in a low-cost multi-core CPU. An overview of the algorithms in charge of implementing this strategy is presented, focusing on wavefront sensing.