Noise-Induced Limitations to the Scalability of Distributed Integral Control

TL;DR

This paper investigates how measurement noise impacts the scalability of distributed integral control in large networked systems, revealing fundamental limitations that favor centralized control in large, sparse networks.

Contribution

It demonstrates that measurement noise diminishes the benefits of distributed integral control as network size grows, highlighting the need for centralized control in large-scale networks.

Findings

Measurement noise reduces performance benefits of distributed integral control.

Performance degrades with increasing network size despite tuning.

Large sparse networks require centralized control for optimal scalability.

Abstract

We study performance limitations of distributed feedback control in large-scale networked dynamical systems. Specifically, we address the question of how the performance of distributed integral control is affected by measurement noise. We consider second-order consensus-like problems modeled over a toric lattice network, and study asymptotic scalings (in network size) of H2 performance metrics that quantify the variance of nodal state fluctuations. While previous studies have shown that distributed integral control fundamentally improves these performance scalings compared to distributed proportional feedback control, our results show that an explicit inclusion of measurement noise leads to the opposite conclusion. The noise's impact on performance is shown to decrease with an increased inter-nodal alignment of the local integral states. However, even though the controller can be tuned for acceptable performance for any given network size, performance will degrade as the network grows, limiting the scalability of any such controller tuning. In particular, the requirement for inter-nodal alignment increases with network size. We show that this in practice implies that large and sparse networks will require any integral control to be centralized, rather than distributed. In this case, the best-achievable performance scaling, which is shown to be that of proportional feedback control, is retrieved.