# Structural accessibility and structural observability of nonlinear networked systems

## TL;DR

This paper extends classical linear notions of controllability and observability to nonlinear networked systems, revealing that nonlinearities can simplify control and observation by reducing the number of variables needed.

## Contribution

It introduces and characterizes the concepts of structural accessibility and observability for nonlinear systems, broadening the applicability of network control theory.

## Key findings

- Nonlinearities facilitate control and observation in networked systems.
- Reduced number of variables needed for control and measurement.
- Enhanced understanding of network structure's role in nonlinear dynamics.

## Abstract

The classical notions of structural controllability and structural observability are receiving increasing attention in Network Science, since they provide a mathematical basis to answer how the network structure of a dynamic system affects its controllability and observability properties. However, these two notions are formulated assuming systems with linear dynamics, which significantly limit their applicability. To overcome this limitation, here we introduce and fully characterize the notions "structural accessibility" and "structural observability" for systems with nonlinear dynamics. We show how nonlinearities make easier the problem of controlling and observing networked systems, reducing the number of variables that are necessary to directly control and directly measure. Our results contribute to understanding better the role that the network structure and nonlinearities play in our ability to control and observe complex dynamic systems.