A Tight Lower Bound on the Controllability of Networks with Multiple Leaders

TL;DR

This paper establishes a precise lower bound on the controllability of networked systems with multiple leaders, using algebraic graph theory to analyze how network topology influences control capabilities.

Contribution

It provides a tight topological lower bound on the controllability matrix rank for networks with arbitrary topologies and multiple leaders, advancing understanding of network controllability.

Findings

Derived a tight lower bound on controllability matrix rank

Applicable to networks with arbitrary topologies and multiple leaders

Enhances understanding of influence propagation in network control

Abstract

In this paper we study the controllability of networked systems with static network topologies using tools from algebraic graph theory. Each agent in the network acts in a decentralized fashion by updating its state in accordance with a nearest-neighbor averaging rule, known as the consensus dynamics. In order to control the system, external control inputs are injected into the so called leader nodes, and the influence is propagated throughout the network. Our main result is a tight topological lower bound on the rank of the controllability matrix for such systems with arbitrary network topologies and possibly multiple leaders.