Properties of the controllability set of one class of differential inclusions

In this paper we consider a mathematical model of control system in the form differential inclusion. The problem of controllability of this system under the condition of mobility of the terminal set $M=M(t)$ is researched. For this model of a dynamic system we define a notion of the $M$-controllability set. Using the methods of the theory of differential inclusions and multi-valued maps, the structural and topological properties of the $M$-controllability set are studied.