Discrete dynamical systems: inverse problems and related topics

In this review, we extend the Boundary Control method\, -- \,an approach to inverse problems based on control theory for dynamical systems \, -- \,to inverse problems for discrete dynamical systems. We apply our results to classical moment problems, Toda lattices, Weyl functions, de Branges spaces, Krein-Stieltjes strings, and also to problems of numerical simulations.