An adaptive telescope with a Hartmann sensor of the wave–front distortions and a phase corrector in the form of a matrix of square–shaped segments is considered. The efficiencies of two algorithms of the corrector control are compared. One of the proposed algorithms is very simple and can be performed without a processor, i.e., with an analog device and hence can provide fast response at a low cost of a corrector control unit. The other algorithm is based on a model representation of the wave–front distortions and uses the least–squares method for seeking for coefficients at the aberration polynomials. The latter algorithm needs for a processor, but provides a diffraction–limited resolution at a sufficient level of the reference signal. The function of the point image diffusion has been calculated for both methods. The averaging was done over random samples of the wave–front distortions generated on a computer.