On one version of approximate permitting control calculation in a problem of approaching

A stationary control system defined on a finite time interval in Euclidean space is considered. We discuss one of the main problems of control theory, which is a problem of approach of a control system and a set in a phase space at a fixed time. This problem is closely connected with key problems in control theory, for example, with a problem of optimal performance. That is why it is necessary to find effective algorithms for solving this task. Due to the complexity of this problem it is impossible to solve it analytically even for simple cases. The construction of approximate solutions considered in this paper is connected with the construction of integral funnel of the control system inverted in time. This work contains the description of one algorithm for the integral funnel construction which is a final approximation of a solvability set for a problem of approach. The procedure of finding solvability control of the approximate solution based on local control saving is described. Illustrating example of a mechanical control system is provided.