Adaptive algorithms for synchronization, consensus of multi-agents and anti-synchronization of direct complex networks

TL;DR

This paper introduces distributed adaptive algorithms for synchronization, consensus, and anti-synchronization in complex networks and multi-agent systems, ensuring invariance of the zero eigenvalue eigenvector of the adaptive coupling matrix.

Contribution

It proposes novel adaptive algorithms that maintain the eigenvector invariance, enabling flexible synchronization, consensus, and anti-synchronization in complex networks.

Findings

Algorithms ensure synchronization and consensus under generalized QUAD conditions.

The methods handle both with and without pinning controllers.

Invariant eigenvector property enhances stability and robustness.

Abstract

In this paper, we discuss distributed adaptive algorithms for synchronization of complex networks, consensus of multi-agents with or without pinning controller. The dynamics of individual node is governed by generalized QUAD condition. We design new algorithms, which can keep the left eigenvector of the adaptive coupling matrix corresponding to the zero eigenvalue invariant. Based on this invariance, various distributive adaptive synchronization, consensus, anti-synchronization models are given.