Flocking estimates for the Cucker-Smale model with time lag and hierarchical leadership

TL;DR

This paper studies the Cucker-Smale flocking model with hierarchical leadership and time delay, proving convergence to consensus despite delays, highlighting the benefits of hierarchical structures in real-world scenarios.

Contribution

It introduces a Lyapunov functional approach to prove consensus in the Cucker-Smale model with hierarchical leadership and time delay, extending previous results to include delays.

Findings

Consensus is achieved for any positive delay.

Hierarchical leadership structure helps counteract delay effects.

The approach can be applied to similar multi-agent systems.

Abstract

We analyze the Cucker-Smale model under hierarchical leadership in presence of a time delay. By using a Lyapunov functional approach and some induction arguments we will prove convergence to consensus for every positive delay $\tau$. These results seem to point out the advantage of a hierarchical structure in order to contrast time delay effects that frequently appear in real situations.