  In the framework of the application of the Boundary Control method to solving
the inverse dynamical problems for the one-dimensional Schr\"odinger and Dirac
operators on the half-line and semi-infinite discrete Schr\"odinger operator,
we establish the connections with the method of De Branges: for each of the
system we construct the De Branges space and give a natural dynamical
interpretation of all its ingredients: the set of function the De Brange space
consists of, the scalar product, the reproducing kernel.
