Controllability of Heterogeneous Multi-Agent Networks

TL;DR

This paper investigates the controllability of heterogeneous multi-agent networks with different agent dynamics and topologies, providing necessary and sufficient conditions for controllability and illustrating the results with examples.

Contribution

It extends controllability analysis to heterogeneous multi-agent networks with multiple dynamics types and different topologies, offering new theoretical conditions.

Findings

Controllability depends on leader-follower connectivity and the existence of a controllable Laplacian combination.

Heterogeneous agents require each to have a controllable dynamic part for the network to be controllable.

Introduces the concept of eigenvector-uncontrollable to analyze partial controllability issues.

Abstract

The existing results on controllability of multi-agents networks are mostly based on homogeneous nodes. This paper focuses on controllability of heterogeneous multi-agent networks, where the agents are modeled as two types. One type is that the agents are of the same high-order dynamics, and the interconnection topologies of the information flow in different orders are supposed to be different. It is proved that a heterogeneous-topology network is controllable if and only if the first-order information topology is leader-follower connected, and there exists a Laplacian matrix, which is a linear combination of the Laplacian matrices of each order information, whose corresponding topology is controllable. The other type is that the agents are of generic linear dynamics, and the dynamics are supposed to be heterogeneous. A necessary and sufficient condition for controllability of heterogeneous-dynamic networks is that each agent contains a controllable dynamic part, and the interconnection topology of the network is leader-follower connected. If some dynamics of the agents are not controllable, the controllability between the agents and the whole network is also studied by introducing the concept of eigenvector-uncontrollable. Different illustrative examples are provided to demonstrate the effectiveness of the theoretical results in this paper.