  The work is carried out as part of the program to construct a new
functio\-nal (so-called {\it wave}) model of symmetric operators. It is shown
that an abstract evolutionary dynamic system of the first order (with respect
to time) with boundary control, which is determined by a symmetric operator
$L_0:{\mathscr H}\to{\mathscr H}$, is controllable if and only if $L_0$ has no
maximal symmetric parts in~${\mathscr H}$.
