Consensus of Multi-agent Systems Under State-dependent Information Transmission

TL;DR

This paper investigates consensus in multi-agent systems with state-dependent switching networks, establishing conditions for consensus under fixed and state-dependent connectivity, with applications to opinion dynamics and rendezvous problems.

Contribution

It introduces new conditions for achieving consensus in multi-agent systems with state-dependent communication networks, including both fixed and vanishing connectivity scenarios.

Findings

Consensus achievable under decay of transmission influence

Initial states influence consensus in state-dependent networks

Applications demonstrated in opinion dynamics and rendezvous models

Abstract

In this paper, we study the consensus problem for continuous-time and discrete-time multi-agent systems in state-dependent switching networks. In each case, we first consider the networks with fixed connectivity, in which the communication between adjacent agents always exists but the influence could possibly become negligible if the transmission distance is long enough. It is obtained that consensus can be reached under a restriction of either the decaying rate of the transmission weight or the initial states of the agents. After then we investigate the networks with state-dependent connectivity, in which the information transmission between adjacent agents gradually vanishes if their distance exceeds a fixed range. In such networks, we prove that the realization of consensus requires the validity of some initial conditions. Finally, the conclusions are applied to models with the transmission law of C-S model, opinion dynamics and the rendezvous problem, the corresponding simulations are also presented.