Noise-induced limitations to the scalability of distributed integral control

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 H 2 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 may in practice imply that very 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.

Scalable robustness of interconnected systems subject to structural changes

“…The effect of external disturbances (sometimes called network performance) has been studied for static interconnected systems in, e.g., Zelazo and Mesbahi (2011), Siami and Motee (2016), and Lovisari et al (2013), whereas Siami and Motee (2018) considers the effects of adding edges in the interconnection structure. An alternative per-spective is given in Bamieh et al (2012) (see also Tegling and Sandberg (2019)), where network performance measures are analysed as a function of the network size, i.e., the number of subsystems, in a property known as coherence. This is thus scalability analysis of network performance.…”