# On resilient control of dynamical flow networks

## TL;DR

This paper reviews recent advances in the stability and robustness of dynamical flow networks, emphasizing monotone models and introducing the concept of margin of resilience to quantify robustness.

## Contribution

It unifies recent results on stability and robustness of dynamical flow networks within a comprehensive framework, highlighting methodological aspects like monotonicity.

## Key findings

- Stability properties of monotone dynamical flow networks are analyzed.
- The notion of margin of resilience is introduced as a robustness measure.
- Connections to road traffic flow models are established.

## Abstract

Resilience has become a key aspect in the design of contemporary infrastructure networks. This comes as a result of ever-increasing loads, limited physical capacity, and fast-growing levels of interconnectedness and complexity due to the recent technological advancements. The problem has motivated a considerable amount of research within the last few years, particularly focused on the dynamical aspects of network flows, complementing more classical static network flow optimization approaches. In this tutorial paper, a class of single-commodity first-order models of dynamical flow networks is considered. A few results recently appeared in the literature and dealing with stability and robustness of dynamical flow networks are gathered and originally presented in a unified framework. In particular, (differential) stability properties of monotone dynamical flow networks are treated in some detail, and the notion of margin of resilience is introduced as a quantitative measure of their robustness. While emphasizing methodological aspects -- including structural properties, such as monotonicity, that enable tractability and scalability -- over the specific applications, connections to well-established road traffic flow models are made.