Controllability of Formations over Time-varying Graphs

TL;DR

This paper studies how the structure of time-varying directed graphs influences the controllability of formation control systems, establishing conditions under which the system can be approximately controlled.

Contribution

It relates graph properties to controllability and demonstrates approximate path-controllability under mild conditions on the graph structure.

Findings

Controllability depends on strongly connected components of the graph.

Approximate path-controllability holds for weakly connected graphs under mild assumptions.

The results connect graph topology with control capabilities in formation systems.

Abstract

In this paper, we investigate the controllability of a class of formation control systems. Given a directed graph, we assign an agent to each of its vertices and let the edges of the graph describe the information flow in the system. We relate the strongly connected components of this graph to the reachable set of the formation control system. Moreover, we show that the formation control model is approximately path-controllable over a path-connected, open dense subset as long as the graph is weakly connected and satisfies some mild assumption on the numbers of vertices of the strongly connected components.