Consensus Seeking in Multi-Agent Systems with Multiplicative Measurement Noises

TL;DR

This paper studies how multi-agent systems reach consensus when agents' measurements are affected by multiplicative noise, providing conditions for convergence and demonstrating effectiveness through simulations.

Contribution

It introduces a novel analysis of consensus in multi-agent systems with multiplicative measurement noise, including convergence conditions and stability results.

Findings

Mean square consensus can be achieved with proper gain selection.

Exponential convergence is proven for fixed network topologies.

Simulations confirm theoretical results and effectiveness.

Abstract

In this paper, the consensus problems of the continuous-time integrator systems under noisy measurements are considered. The measurement noises, which appear when agents measure their neighbors' states, are modeled to be multiplicative. By multiplication of the noises, here, the noise intensities are proportional to the absolute value of the relative states of agent and its neighbor. By using known distributed protocols for integrator agent systems, the closed-loop {system is} described in the vector form by a singular stochastic differential equation. For the fixed and switching network topologies cases, constant consensus gains are properly selected, such that mean square consensus and strong consensus can be achieved. Especially, exponential mean square convergence of agents' states to the common value is derived for the fixed topology case. In addition, asymptotic unbiased mean square average consensus and asymptotic unbiased strong average consensus are also studied. Simulations shed light on the effectiveness of the proposed theoretical results.