Single module identifiability in linear dynamic networks with partial excitation and measurement

Identifiability of a single module in a network of transfer functions is determined by whether a particular transfer function in the network can be uniquely distinguished within a network model set, on the basis of data. Whereas previous research has focused on the situations that all network signals are either excited or measured, we develop generalized analysis results for the situation of partial measurement and partial excitation. As identifiability conditions typically require a sufficient number of external excitation signals, this article introduces a novel network model structure such that excitation from unmeasured noise signals is included, which leads to less conservative identifiability conditions than relying on measured excitation signals only. More importantly, graphical conditions are developed to verify global and generic identifiability of a single module based on the topology of the dynamic network. Depending on whether the input or the output of the module can be measured, we present four identifiability conditions which cover all possible situations in single module identification. These conditions further lead to synthesis approaches for allocating excitation signals and selecting measured signals, to warrant single module identifiability. In addition, if the identifiability conditions are satisfied for a sufficient number of external excitation signals only, indirect identification methods are developed to provide a consistent estimate of the module. All the obtained results are also extended to identifiability of multiple modules in the network.</p

Exploiting unmeasured disturbance signals in identifiability of linear dynamic networks with partial measurement and partial excitation

Identifiability conditions for networks of transfer functions require a sucientnumber of external excitation signals, which are typically measured reference signals. In this abstract, we introduce an equivalent network model structure to address the contribution of unmeasured noises to identifiability analysis in the setting with partial excitation and partial measurement. With this model structure, unmeasured disturbance signals can be exploited as excitation sources, which leads to less conservative identifiability conditions

On Data-Driven Control: Informativity of Noisy Input-Output Data With Cross-Covariance Bounds

In this letter we develop new data informativity based controller synthesis methods that extend existing frameworks in two relevant directions: a more general noise characterization in terms of cross-covariance bounds and informativity conditions for control based on input-output data. Previous works have derived necessary and sufficient informativity conditions for noisy input-state data with quadratic noise bounds via an S-procedure. Although these bounds do not capture cross-covariance bounds in general, we show that the S-procedure is still applicable for obtaining non-conservative conditions on the data. Informativity-conditions for stability, H and H2 control are developed, which are sufficient for input-output data and also necessary for input-state data. Simulation experiments illustrate that cross-covariance bounds can be less conservative for informativity, compared to norm bounds typically employed in the literature.</p

A Necessary Condition for Network Identifiability With Partial Excitation and Measurement

This article considers dynamic networks where vertices and edges represent manifest signals and causal dependencies among the signals, respectively. We address the problem of how to determine if the dynamics of a network can be identified when only partial vertices are measured and excited. A necessary condition for network identifiability is presented, where the analysis is performed based on identifying the dependency of a set of rational functions from excited vertices to measured ones. This condition is further characterized by using an edge-removal procedure on the associated bipartite graph. Moreover, on the basis of necessity analysis, we provide a necessary and sufficient condition for identifiability in circular networks.</p

Genome-wide identification of directed gene networks using large-scale population genomics data

Identification of causal drivers behind regulatory gene networks is crucial in understanding gene function. Here, we develop a method for the large-scale inference of gene–gene interactions in observational population genomics data that are both directed (using local genetic instruments as causal anchors, akin to Mendelian Randomization) and specific (by controlling for linkage disequilibrium and pleiotropy). Analysis of genotype and whole-blood RNA-sequencing data from 3072 individuals identified 49 genes as drivers of downstream transcriptional changes (Wald P < 7 × 10−10), among which transcription factors were overrepresented (Fisher’s P = 3.3 × 10−7). Our analysis suggests new gene functions and targets, including for SENP7 (zinc-finger genes involved in retroviral repression) and BCL2A1 (target genes possibly involved in auditory dysfunction). Our work highlights the utility of population genomics data in deriving directed gene expression networks. A resource of trans-effects for all 6600 genes with a genetic instrument can be explored individually using a web-based browser

Identification of diffusively coupled linear networks through structured polynomial models

Physical dynamic networks most commonly consist of interconnections of physical components that can be described by diffusive couplings. These diffusive couplings imply that the cause-effect relationships in the interconnections are symmetric, and therefore, physical dynamic networks can be represented by undirected graphs. This article shows how prediction error identification methods developed for linear time-invariant systems in polynomial form can be configured to consistently identify the parameters and the interconnection structure of diffusively coupled networks. Furthermore, a multistep least squares convex optimization algorithm is developed to solve the nonconvex optimization problem that results from the identification method.</p

On representations of linear dynamic networks

Linear dynamic networks are typically described in either a state-space form or a module representation. The question is addressed under which conditions these representations are equivalent and can be transformed into one another. Hidden states and especially shared hidden states have a central position in this analysis. A consequence for identification is that MIMO parameterised modules may be necessary in order to appropriately take care of shared hidden states. Further, the construction of sub-networks in a linear dynamic network resulting in a module representation is illustrated. The module dynamic network allows to zoom in/out on/of the network to include/exclude more detailed structural information. Zooming in and out is respectively described by realisation and multi-path immersion