Handling unmeasured disturbances in data-driven distributed control with virtual reference feedback tuning

The data-driven synthesis of a distributed controller in the presence of noise is considered, via the distributed virtual reference feedback tuning (DVRFT) framework. The analysis is performed for a linear interconnected system on an arbitrary graph that is subject to unmeasured exogenous inputs. By solving a dynamic network identification problem with prediction-error filtering and a tailor-made noise model, we show that the distributed model-reference control problem can be solved directly from data. Sufficient conditions are provided for which the local controller estimates are consistent. Moreover, it is shown how the method can be applied in the single-input-single-output case, leading to consistent estimates with standard virtual reference feedback tuning as well. The effectiveness of the method is demonstrated via a small network example with two interconnected systems.