Multi-Agent Consensus With Relative-State-Dependent Measurement Noises

TL;DR

This paper investigates distributed consensus in multi-agent systems with measurement noises dependent on agents' relative states, providing conditions for convergence and analyzing the effects of noise on consensus.

Contribution

It develops new consensus theorems considering relative-state-dependent noises, including necessary and sufficient conditions for mean square consensus.

Findings

Consensus gain thresholds depend only on the number of agents and noise coefficient.

Conditions for mean square and almost sure consensus are established.

Convergence rate is estimated using Brownian motion laws.

Abstract

In this note, the distributed consensus corrupted by relative-state-dependent measurement noises is considered. Each agent can measure or receive its neighbors' state information with random noises, whose intensity is a vector function of agents' relative states. By investigating the structure of this interaction and the tools of stochastic differential equations, we develop several small consensus gain theorems to give sufficient conditions in terms of the control gain, the number of agents and the noise intensity function to ensure mean square (m. s.) and almost sure (a. s.) consensus and quantify the convergence rate and the steady-state error. Especially, for the case with homogeneous communication and control channels, a necessary and sufficient condition to ensure m. s. consensus on the control gain is given and it is shown that the control gain is independent of the specific network topology, but only depends on the number of nodes and the noise coefficient constant. For symmetric measurement models, the almost sure convergence rate is estimated by the Iterated Logarithm Law of Brownian motions.