Local module identification in dynamic networks: do more inputs guarantee smaller variance?

TL;DR

This paper investigates how the choice and number of predictor inputs affect the variance of local module estimates in dynamic networks, showing that fewer inputs can sometimes lead to more accurate estimates.

Contribution

It analyzes the impact of input selection on variance reduction in local module identification, comparing full-MISO and immersed network approaches for the first time.

Findings

Fewer predictor inputs can reduce variance under certain conditions.

Immersed network approach can outperform full-MISO in variance reduction.

Case study confirms theoretical insights with practical implications.

Abstract

Recent developments in science and engineering have motivated control systems to be considered as interconnected and networked systems. From a system identification point of view, modelling of a local module in such a structured system is a relevant and interesting problem. This work focuses on the quality, in terms of variance, of an estimate of a local module. We analyse which predictor input signals are relevant and contribute to variance reduction, while still guaranteeing the consistency of the estimate. For a targeted local module, a comparison of its estimate variance is made between a full-MISO approach and an immersed network setting, where a reduced number of inputs is used, while still guaranteeing consistency. A case study of a four-node network is considered and it is shown that a smaller set of predictor inputs can, under some conditions, result in a smaller variance compared to the full-MISO approach.