УПРАВЛЯЕМОСТЬ НЕЛИНЕЙНЫХ СИСТЕМ СО СМЕНОЙ ФАЗОВОГО ПРОСТРАНСТВА

В настоящей работе исследуется дифференциальная управляемая система следующей структуры: на двух последовательных отрезках времени движение объекта описывается двумя различными системами дифференциальных уравнений. Рассматривается вопрос перевода объекта из заданного множества одного пространства в заданное множество другого пространства. При этом пространства могут быть одной размерности, а также возможен переход как из пространства большей размерности в пространство меньшей размерности, так и наоборот.

The problems with changing phase space are a subclass of the so-called hybrid (composite) systems. They are characterized by the fact that at different time intervals they are described by different differential systems and certain links for the connection of the trajectories. The systems can have the similar dimensionality and also the transfer both from the dimension with the higher dimensionality to the lower dimensionality and vice versa. The original source of such problems were the multistage processes of space flights. This work researches the task of controllability of the object, described by the predetermined system, from the initial set of one dimension to the predetermined set of another dimension through the null point. The transfer of the object from one dimension to another dimension is giver by certain mapping. Thus, in the first space, the movement of an object is described by the so-called triangular systems. Triangular systems are one of the most important classes of nonlinear systems that allow mapping to linear systems. In the second space, the movement of the object is described by a nonlinear system with control actions of a special kind. The control action has a special structure due to physical applications. For the problem in which the nonlinear triangular system in the initial space is fully controllable and the nonlinear system in the second space is locally null-controlled the sufficient controllability conditions are achieved. Both nonlinear systems have physical applications. Taking into account the applicative manner of the given problem the results achieved in this work are of both theoretical and practical significance.