Fully distributed consensus control for stochastic multi-agent systems under undirected and directed topologies

TL;DR

This paper develops fully distributed control protocols for stochastic multi-agent systems, ensuring consensus under both undirected and directed topologies, with proven solution existence, uniqueness, and convergence rates.

Contribution

It introduces the first unified distributed control protocol for directed graphs and an enhanced protocol for undirected graphs with tunable parameters.

Findings

Established existence and uniqueness of solutions for nonlinear stochastic systems.

Designed a unified control protocol guaranteeing mean square and almost sure consensus.

Provided explicit exponential convergence rate estimates.

Abstract

This work aims to address the design of fully distributed control protocols for stochastic consensus, and, for the first time, establishes the existence and uniqueness of solutions for the path-dependent and highly nonlinear closed-loop systems under both undirected and directed topologies, bridging a critical gap in the literature. For the case of directed graphs, a unified fully distributed control protocol is designed for the first time to guarantee mean square and almost sure consensus of stochastic multi-agent systems under directed graphs. Moreover, an enhanced fully distributed protocol with additional tunable parameters designed for undirected graphs is proposed, which guarantees stochastic consensus while achieving superior convergence speed. Additionally, our work provides explicit exponential estimates for the corresponding convergence rates of stochastic consensus, elucidating the relationship between the exponential convergence rate and the system parameters. Simulations validate the theoretical results.