Perfectly Controllable Multi-Agent Networks

TL;DR

This paper introduces the concept of perfect controllability in multi-agent networks, providing a necessary and sufficient condition and a constructive design method for topologies that remain controllable regardless of leader selection.

Contribution

It defines perfect controllability, derives a condition for it, and proposes a step-by-step topology design procedure applicable for any number and placement of leaders.

Findings

A necessary and sufficient condition for perfect controllability is established.

A constructive design method for topologies ensuring perfect controllability is proposed.

The method is validated for arbitrary leader numbers and positions.

Abstract

This note investigates how to design topology structures to ensure the controllability of multi-agent networks (MASs) under any selection of leaders. We put forward a concept of perfect controllability, which means that a multi-agent system is controllable with no matter how the leaders are chosen. In this situation, both the number and the locations of leader agents are arbitrary. A necessary and sufficient condition is derived for the perfect controllability. Moreover, a step-by-step design procedure is proposed by which topologies are constructed and are proved to be perfectly controllable. The principle of the proposed design method is interpreted by schematic diagrams along with the corresponding topology structures from simple to complex. We show that the results are valid for any number and any location of leaders. Both the construction process and the corresponding topology structures are clearly outlined.