Arne G. Dankers

Harm Weerts, Paul M. J. Van den Hof, Arne Dankers

A recent development in data-driven modelling addresses the problem of identifying dynamic models of interconnected systems, represented as linear dynamic networks. For these networks the notion network identifiability has been introduced recently, which reflects the property that different network models can be distinguished from each other. Network identifiability is extended to cover the uniqueness of a single module in the network model. Conditions for single module identifiability are derived and formulated in terms of path-based topological properties of the network models.

Paul M. J. Van den Hof, Karthik R. Ramaswamy, Arne G. Dankers et al.

The identification of local modules in dynamic networks with known topology has recently been addressed by formulating conditions for arriving at consistent estimates of the module dynamics, typically under the assumption of having disturbances that are uncorrelated over the different nodes. The conditions typically reflect the selection of a set of node signals that are taken as predictor inputs in a MISO identification setup. In this paper an extension is made to arrive at an identification setup for the situation that process noises on the different node signals can be correlated with each other. In this situation the local module may need to be embedded in a MIMO identification setup for arriving at a consistent estimate with maximum likelihood properties. This requires the proper treatment of confounding variables. The result is an algorithm that, based on the given network topology and disturbance correlation structure, selects an appropriate set of node signals as predictor inputs and outputs in a MISO or MIMO identification setup. As a first step in the analysis, we restrict attention to the (slightly conservative) situation where the selected output node signals are predicted based on all of their in-neighbor node signals in the network.

Paul M. J. Van den Hof, Shengling Shi, Stefanie J. M. Fonken et al.

When estimating a single subsystem (module) in a linear dynamic network with a prediction error method, a data-informativity condition needs to be satisfied for arriving at a consistent module estimate. This concerns a condition on input signals in the constructed, possibly MIMO (multiple input multiple output) predictor model being persistently exciting, which is typically guaranteed if the input spectrum is positive definite for a sufficient number of frequencies. Generically, the condition can be formulated as a path-based condition on the graph of the network model. The current condition has two elements of possible conservatism: (a) rather than focussing on the full MIMO model, one would like to be able to focus on consistently estimating the target module only, and (b) structural information, such as structural zero elements in the interconnection structure or known subsystems, should be taken into account. In this paper relaxed conditions for data-informativity are derived addressing these two issues, leading to relaxed path-based conditions on the network graph. This leads to experimental conditions that are less strict, i.e. require a smaller number of external excitation signals. Additionally, the new expressions for data-informativity in identification are shown to be closely related to earlier derived conditions for (generic) single module identifiability.