Scale-free weak output synchronization of multi-agent systems with adaptive protocols

TL;DR

This paper develops adaptive protocols for multi-agent systems that achieve scale-free output synchronization, including weak synchronization, without requiring network knowledge, applicable to both collaborative and non-collaborative settings.

Contribution

It introduces adaptive protocols that ensure scale-free synchronization in multi-agent systems, handling directed networks and weak synchronization scenarios.

Findings

Protocols achieve classical synchronization with directed spanning trees.

Protocols induce weak synchronization when the network lacks a spanning tree.

Applicable to both collaborative and non-collaborative multi-agent systems.

Abstract

In this paper, we study output synchronization for multi-agent systems. The objective is to design a protocol which only depends on the agent dynamics and does not require any knowledge of the network. If the network has a directed spanning tree then the protocols designed in this paper achieve classical output synchronization. Otherwise, the protocol achieves weak synchronization which is induced by network stability in the sense that the signals exchanged over the network converge to zero. Weak sychronization is explained in detail in this paper. Even though we consider linear agents, it is known that this in general requires nonlinear protocols. In the paper we use adaptive protocols. In the literature, two classes of protocols are considered often called collaborative protocols (with additional communication between the protocols and non-collaborative protocols (sometimes referred to as fully decentralized where the additional communication is not present). This paper considers both of these cases.