Approaches to constructing algorithms for controlling adaptive optics (AO) systems based on prediction of evolutions of spatial and temporal distributions of phase distortions in the optical wave propagating in an atmospheric turbulence and generation of control signals for correcting wavefront distortions in real time are described. Main patterns of evolutions of phase distortions of optical waves propagating in the Kolmogorov-type turbulent atmosphere are analyzed. An extremely high operating frequency of the Shack–Hartmann-type wavefront sensor has been estimated. Numerical modeling of the AO system operation has been performed in closed and open tracking loops. Errors in estimating the turbulence parameters with the wavefront sensor operating at high frequencies are given.