Time scale design for network resilience

TL;DR

This paper introduces a framework for designing time scales in networked systems with multi-time scale consensus dynamics to optimize network resilience by minimizing the $ ext{H}_2$-norm, accounting for edge weights, noise, and independent agent time scales.

Contribution

It presents a novel general framework for multi-time scale network systems and a method for designing time scales to enhance resilience by minimizing the $ ext{H}_2$-norm.

Findings

Separation of weighting and scaling influences in the design problem.

Framework accommodates edge weights, noise, and independent agent time scales.

Method improves network resilience by optimal time scale design.

Abstract

In this paper we consider the $\mathcal{H}_2$-norm of networked systems with multi-time scale consensus dynamics. We develop a general framework for such systems that allows for edge weighting, independent agent-based time scales, as well as measurement and process noise. From this general system description, we highlight an interesting case where the influences of the weighting and scaling can be separated in the design problem. We then consider the design of the time scale parameters for minimizing the $\mathcal{H}_2$-norm for the purpose of network resilience.