Local Controllability in the Problem with Phase Space Change

This work researches the problem of controllability with phase space change. Nowadays theinterest to the controllability problems with variable structure is on the rise due to the continuouswidening of their practical application space. The tasks of this sort are appearing in physics,biology as well as in economics. The problem of transfer of object from the constrain set of onespace to the constrain set of different space through the null point at the given lengths of timeis examined. The spaces may be of the different dimensionality. The transfer is possible bothfrom the space of higher dimensionality to the space of lower dimensionality and vice versa. Themovement of the object is described by two nonlinear systems of differential equations, whilethe control action of the first system has a special form, due to some physical applications. Thetransfer of the object from one space to another is given by certain mapping. For the problemin which the nonlinear system in the initial space is locally null-controlled and the right partof differential inclusion in the second space is the concave mapping the sufficient controllabilityconditions were achieved. The problem is researched using the controllability theory apparatus,convex analysis and multiple-valued mapping theory. Taking into the account the practical valueof the given problem the results achieved are of both theoretical and practical significance.