Prediction error identification of linear dynamic networks with rank-reduced noise

Dynamic networks are interconnected dynamic systems with measured node signals and dynamic modules reflecting the links between the nodes. We address the problem of \red{identifying a dynamic network with known topology, on the basis of measured signals}, for the situation of additive process noise on the node signals that is spatially correlated and that is allowed to have a spectral density that is singular. A prediction error approach is followed in which all node signals in the network are jointly predicted. The resulting joint-direct identification method, generalizes the classical direct method for closed-loop identification to handle situations of mutually correlated noise on inputs and outputs. When applied to general dynamic networks with rank-reduced noise, it appears that the natural identification criterion becomes a weighted LS criterion that is subject to a constraint. This constrained criterion is shown to lead to maximum likelihood estimates of the dynamic network and therefore to minimum variance properties, reaching the Cramer-Rao lower bound in the case of Gaussian noise.Comment: 17 pages, 5 figures, revision submitted for publication in Automatica, 4 April 201

Abstractions of linear dynamic networks for input selection in local module identification

In abstractions of linear dynamic networks, selected node signals are removed from the network, while keeping the remaining node signals invariant. The topology and link dynamics, or modules, of an abstracted network will generally be changed compared to the original network. Abstractions of dynamic networks can be used to select an appropriate set of node signals that are to be measured, on the basis of which a particular local module can be estimated. A method is introduced for network abstraction that generalizes previously introduced algorithms, as e.g. immersion and the method of indirect inputs. For this abstraction method it is shown under which conditions on the selected signals a particular module will remain invariant. This leads to sets of conditions on selected measured node variables that allow identification of the target module.Comment: 17 pages, 7 figures. Paper to appear in Automatica, Vol. 117, July 202