Optimal Control of Networks in the presence of Attackers and Defenders

TL;DR

This paper formulates an optimal control framework for defending dynamical networks against localized attacks, considering network topology and attacker/defender placement to minimize control energy.

Contribution

It introduces a novel optimal control approach that accounts for network structure and attacker-defender distribution to enhance network resilience.

Findings

Optimal defense strategies depend on network topology.

Control energy varies with attacker and defender placement.

Different network types require tailored defense approaches.

Abstract

We consider the problem of a dynamical network whose dynamics is subject to external perturbations (`attacks') locally applied at a subset of the network nodes. We assume that the network has an ability to defend itself against attacks with appropriate countermeasures, which we model as actuators located at (another) subset of the network nodes. We derive the optimal defense strategy as an optimal control problem. We see that the network topology, as well as the distribution of attackers and defenders over the network affect the optimal control solution and the minimum control energy. We study the optimal control defense strategy for several network topologies, including chain networks, star networks, ring networks, and scale free networks.