First and second-order Cucker-Smale models with non-universal interaction, time delay and communication failures

TL;DR

This paper analyzes first and second-order Cucker-Smale alignment models with non-universal interactions, time delays, and communication failures, establishing conditions for exponential consensus convergence in complex networked systems.

Contribution

It introduces a framework for analyzing alignment models with non-universal, delayed, and intermittent interactions using graph topology and persistence excitation conditions.

Findings

Exponential convergence to consensus under strong connectivity.

Effective handling of time delays and communication failures.

Applicability to complex networked multi-agent systems.

Abstract

In this paper, we deal with first and second-order alignment models with non-universal interaction, time delay and possible lack of connection between the agents. More precisely, we analyze the situation in which the system's agents do not transmit information to all the other agents and also agents that are linked to each other can suspend their interaction at certain times. Moreover, we take into account of possible time lags in the interactions. To deal with the considered "non-universal" connection, a graph topology over the structure of the model has to be considered. Under a so-called Persistence Excitation Condition, we establish the exponential convergence to consensus for both models whenever the digraph that describes the interaction between the agents is strongly connected.