The paper considers an artificial Earth satellite moving in a Keplerian circular orbit of arbitrary inclination. To stabilize the angular position of the satellite in the orbital coordinate system, an electrodynamic attitude control system is used based on the simultaneous use of two control torques-the Lorentz torque and the torque of magnetic interaction. The problem of stabilizing the satellite in the straight equilibrium position is solved, taking into account the influence of the disturbing effect of the gravitational torque. The decision is made in two stages. At the first stage, using the Monte Carlo method, the gain coefficients included in the expressions for the control torques are selected, and at the second stage, the neural network is trained based on previously found controls. The found controls are compared with similar controls previously constructed analytically. The effectiveness of the proposed approach is shown. The convergence of the control process to program motion under any randomly set initial conditions from a wide range is demonstrated.