Structural Controllability of a Consensus Network with Multiple Leaders

TL;DR

This paper establishes that leader-follower connectivity is both necessary and sufficient for the structural controllability of a consensus network with multiple leaders, providing a graph-theoretic criterion for control design.

Contribution

It proves a graph-theoretic condition for structural controllability in multi-leader consensus networks, extending previous results to multiple leaders and considering matrix dependencies.

Findings

Leader-follower connectivity is necessary and sufficient for controllability.

The condition simplifies to graph connectivity when there is a single leader.

The approach explicitly accounts for matrix dependencies using linear parameterization.

Abstract

This paper examines the structural controllability for a group of agents, called followers, connected to each other based on the consensus law under commands of multiple leaders, which are agents with superior capabilities, over a fixed communication topology. It is proved that the graph-theoretic sufficient and necessary condition for the set of followers to be structurally controllable under the leaders' commands is leader-follower connectivity of the associated graph topology. This shrinks to graph connectivity for the case of solo leader. In the approach, we explicitly put into account the dependence among the entries of the system matrices for a consensus network using the linear parameterization technique introduced in [1].