# Abstractions of linear dynamic networks for input selection in local module identification

## TL;DR

This paper presents a generalized method for abstracting linear dynamic networks, enabling effective input selection for local module identification by ensuring certain modules remain invariant under abstraction.

## Contribution

It introduces a new abstraction method that generalizes existing algorithms and provides conditions for invariant modules, aiding targeted network identification.

## Key findings

- The method generalizes previous algorithms like immersion and indirect inputs.
- Conditions are derived for selected signals to keep specific modules invariant.
- The approach facilitates accurate local module estimation through optimal input selection.

## Abstract

In abstractions of linear dynamic networks, selected node signals are removed from the network, while keeping the remaining node signals invariant. The topology and link dynamics, or modules, of an abstracted network will generally be changed compared to the original network. Abstractions of dynamic networks can be used to select an appropriate set of node signals that are to be measured, on the basis of which a particular local module can be estimated. A method is introduced for network abstraction that generalizes previously introduced algorithms, as e.g. immersion and the method of indirect inputs. For this abstraction method it is shown under which conditions on the selected signals a particular module will remain invariant. This leads to sets of conditions on selected measured node variables that allow identification of the target module.