Control technique for synchronization of selected nodes in directed networks

TL;DR

This paper introduces a control method for directing specific nodes in directed networks to follow a desired synchronous trajectory by modifying network topology through distributed controllers, optimizing link adjustments.

Contribution

It presents a novel approach to control arbitrary nodes in directed networks by creating outer symmetries via topology modification and formulates an optimization algorithm for controller selection.

Findings

Successfully controls selected nodes to synchronize with a target trajectory.

Optimizes the number of links added or removed for control implementation.

Provides a systematic method for topology-based control in directed networks.

Abstract

In this Letter we propose a method to control a set of arbitrary nodes in a directed network such that they follow a synchronous trajectory which is, in general, not shared by the other units of the network. The problem is inspired to those natural or artificial networks whose proper operating conditions are associated to the presence of clusters of synchronous nodes. Our proposed method is based on the introduction of distributed controllers that modify the topology of the connections in order to generate outer symmetries in the nodes to be controlled. An optimization problem for the selection of the controllers, which includes as a special case the minimization of the number of the links added or removed, is also formulated and an algorithm for its solution is introduced.