Structurally Robust Control of Complex Networks

TL;DR

This paper introduces a new framework for structurally robust control of complex networks, demonstrating that robustness can be achieved with minimal additional controllers by adjusting network parameters, applicable to real-world unreliable systems.

Contribution

It presents the concept of structurally robust control, providing analytical tools and algorithms to maintain control in networks despite structural uncertainties and failures.

Findings

Robust control is achievable in scale-free networks with the same number of controllers as non-robust networks.

Adjusting the minimum degree of the network ensures robustness against structural failures.

The methodology applies to real systems, such as neural networks with unreliable links.

Abstract

Robust control theory has been successfully applied to numerous real-world problems using a small set of devices called {\it controllers}. However, the real systems represented by networks contain unreliable components and modern robust control engineering has not addressed the problem of structural changes on a large network. Here, we introduce the concept of structurally robust control of complex networks and provide a concrete example using an algorithmic framework that is widely applied in engineering. The developed analytical tools, computer simulations and real network analyses lead herein to the discovery that robust control can be achieved in scale-free networks with exactly the same order of controllers required in a standard non-robust configuration by adjusting only the minimum degree. The presented methodology also addresses the probabilistic failure of links in real systems, such as neural synaptic unreliability in {\it C. elegans}, and suggests a new direction to pursue in studies of complex networks in which control theory has a role.