On solving approach problems for control systems

We study the problem of making a control system in a finite-dimensional Euclidean space approach a compact set at a fixed instant of time. The technique presented in the paper for solving the approach problem is based on constructions involving solvability sets. To construct approximately the solvability set, we apply a backward (in time) procedure that involves storing controls selected during the construction of this set. We also give examples of simulation of approach problems for mechanical systems.