Two-channel optimal discrete law of control of spacecraft with aerodynamic and inertial asymmetry during descent in Mars atmosphere

At present, spacecraft attitude stability is of great importance for both state and private space companies and agencies. In this paper, we consider a mathematical model describing perturbed motion of spacecraft as a rigid body with significant aerodynamic and inertial asymmetry relative to the center of mass in the rarefied atmosphere of Mars. The aim of this work is to obtain an approximate discrete optimized law of controlling the spacecraft attitude using Bellman's dynamic programming and averaging methods. Discrete systems of equations used in the work were solved using the Z-transform method. The reliability of the obtained control laws was confirmed by the results of numerical integration by the numerical Euler method.