Local module identification in dynamic networks: do more inputs guarantee smaller variance?
For researchers in system identification of networked systems, this work provides insight into input selection for variance reduction, though it is an incremental contribution based on a specific case study.
The paper analyzes variance of local module estimates in dynamic networks, showing that using fewer predictor inputs can, under certain conditions, yield smaller variance than using all inputs, as demonstrated in a four-node network case study.
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.