On the stability of direct algorithms for computing programmed controls in nonlinear systems

The results of analysis of qualitative properties of an algorithm of numerical implementation of a new direct method of constructing of an approximate solution in the classical problem of programmed control of a given motion of nonlinear objects are presented. The stability of the direct algorithm to small changes of initial data (good conditionality property) of the direct method is established. In the routing problem for a telescope, carrying flexible panels of solar batteries, the robustness of the programmed control law, computed by the direct method by using a model of the telescope as a solid, is demonstrated numerically.