Graph-Theoretic Characterizations of Structural Controllability for Multi-Agent System with Switching Topology

TL;DR

This paper provides graph-theoretic conditions for the structural controllability of multi-agent systems with switching topologies, showing that connectivity of the union graph determines controllability.

Contribution

It introduces novel graph-theoretic characterizations for the structural controllability of multi-agent systems under switching topologies.

Findings

Controllability depends on the connectivity of the union graph.

Single leader systems are controllable if the union graph is connected.

Multi-leader systems are controllable if the union graph is leader-follower connected.

Abstract

This paper considers the controllability problem for multi-agent systems. In particular, the structural controllability of multi-agent systems under switching topologies is investigated. The structural controllability of multi-agent systems is a generalization of the traditional controllability concept for dynamical systems, and purely based on the communication topologies among agents. The main contributions of the paper are graph-theoretic characterizations of the structural controllability for multi-agent systems. It turns out that the multi-agent system with switching topology is structurally controllable if and only if the union graph G of the underlying communication topologies is connected (single leader) or leader-follower connected (multi-leader). Finally, the paper concludes with several illustrative examples and discussions of the results and future work.