Discrete dynamical systems: inverse problems and related topics

TL;DR

This paper reviews the extension of the Boundary Control method to inverse problems for discrete dynamical systems, covering theoretical developments and applications to classical problems and numerical simulations.

Contribution

It introduces a novel extension of the Boundary Control method to discrete systems and applies it to various classical inverse problems and numerical methods.

Findings

Extended Boundary Control method to discrete systems

Applied to classical moment problems and Toda lattices

Demonstrated effectiveness in numerical simulations

Abstract

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.