Originally, protocols were designed for multi-agent systems (MAS) using information about the network which might not be available. Recently, there has been a focus on scale-free synchronization where the protocol is designed without any prior information about the network. As long as the network contains a directed spanning tree, a scale-free protocol guarantees that the network achieves synchronization. If there is no directed spanning tree then synchronization cannot be achieved. But what happens when these scale-free protocols are applied to such a network where the directed spanning tree no longer exists? This paper establishes that the network decomposes into a number of basic bicomponents which achieves synchronization among all nodes in this basic bicomponent. On the other hand, nodes which are not part of any basic bicomponent converge to a weighted average of the synchronized trajectories of the basic bicomponents. The weights are independent of the initial conditions and are independent of the designed protocol.
@article{arxiv.2403.18200,
title = {Fault-tolerant properties of scale-free linear protocols for synchronization of homogeneous multi-agent systems},
author = {Anton A. Stoorvogel and Ali Saberi and Zhenwei Liu},
journal= {arXiv preprint arXiv:2403.18200},
year = {2024}
}
Comments
The article was submitted to IEEE Transactions on Automatic Control at March 27th, 2024. Now, this updated version is the one re-submitted at October 7th, 2024 for second-round review