Energy Scaling of Targeted Optimal Control of Complex Networks

TL;DR

This paper demonstrates that controlling a subset of nodes in a complex network significantly reduces the energy needed for control, with energy requirements decreasing exponentially as the number of target nodes increases.

Contribution

It introduces a novel approach of controlling node states rather than all nodes, showing substantial energy savings and providing an energy scaling law for network control.

Findings

Energy decays exponentially with the number of target nodes.

Controlling a subset of nodes reduces control energy dramatically.

The energy scaling law applies across various network types and control scenarios.

Abstract

Recently it has been shown that the control energy required to control a dynamical complex network is prohibitively large when there are only a few control inputs. Most methods to reduce the control energy have focused on where, in the network, to place additional control inputs. Here, in contrast, we show that by controlling the states of a subset of the nodes of a network, rather than the state of every node, while holding the number of control signals constant, the required energy to control a portion of the network can be reduced substantially. The energy requirements exponentially decay with the number of target nodes, suggesting that large networks can be controlled by a relatively small number of inputs as long as the target set is appropriately sized. We validate our conclusions in model and real networks to arrive at an energy scaling law to better design control objectives regardless of system size, energy restrictions, state restrictions, input node choices and target node choices.