Aggregate Fluctuations in Networks with Drift-Diffusion Models Driven by Stable Non-Gaussian Disturbances

TL;DR

This paper investigates how multiagent networks driven by heavy-tailed alpha-stable noise exhibit aggregate fluctuations, providing bounds and insights that challenge Gaussian-based design assumptions.

Contribution

It introduces a measure of aggregate fluctuation for networks with alpha-stable noise and derives bounds relating these fluctuations to network spectra and noise statistics.

Findings

Derived upper bounds on aggregate fluctuations using Laplacian spectrum

Showed Gaussian-based algorithms are suboptimal for non-Gaussian noise

Highlighted the impact of heavy-tailed noise on network stability

Abstract

The focus of this paper is to quantify measures of aggregate fluctuations for a class of consensus-seeking multiagent networks subject to exogenous noise with alpha-stable distributions. This type of noise is generated by a class of random measures with heavy-tailed probability distributions. We define a cumulative scale parameter using scale parameters of probability distributions of the output variables, as a measure of aggregate fluctuation. Although this class of measures can be characterized implicitly in closed-form in steady-state, finding their explicit forms in terms of network parameters is, in general, almost impossible. We obtain several tractable upper bounds in terms of Laplacian spectrum and statistics of the input noise. Our results suggest that relying on Gaussian-based optimal design algorithms will result in non-optimal solutions for networks that are driven by non-Gaussian noise inputs with alpha-stable distributions. The manuscript has been submitted for publication to IEEE Transactions on Control of Network Systems. It is the extended version of preliminary paper included in the proceedings of the 2018 American Control Conference.