Controllability of the nonlinear systems with phase space change.

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.

Key words: controllability, local controllability, phase space change, triangular system, full
controllability.