Identification and Prediction in Dynamic Networks with Unobservable Nodes

Linder, Jonas; Enqvist, Martin

doi:10.1016/j.ifacol.2017.08.1306

Cited by 15 publications

(22 citation statements)

References 11 publications

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“…Consider first a network with 3 unknown transfer functions represented in Figure 1 and its corresponding true G 0 and true T 0 . Calculations based on (10) show that identification of all 3 transfer functions requires the measurement of nodes 2 AND 3, and that measuring node 1 yields no information.…”

Section: Motivating Examplesmentioning

confidence: 99%

Identifiability of Dynamical Networks With Partial Node Measurements

Hendrickx

Gevers

Bazanella

2019

IEEE Trans. Automat. Contr.

206

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Much recent research has dealt with the identifiability of a dynamical network in which the node signals are connected by causal linear transfer functions and are excited by known external excitation signals and/or unknown noise signals. A major research question concerns the identifiability of the whole network -topology and all transfer functions -from the measured node signals and external excitation signals. So far all results on this topic have assumed that all node signals are measured. This paper presents the first results for the situation where not all node signals are measurable, under the assumptions that (1) the topology of the network is known, and (2) each node is excited by a known external excitation. Using graph theoretical properties, we show that the transfer functions that can be identified depend essentially on the topology of the paths linking the corresponding vertices to the measured nodes. A practical outcome is that, under those assumptions, a network can often be identified using only a small subset of node measurements.

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Section: Motivating Examplesmentioning

confidence: 99%

Identifiability of Dynamical Networks With Partial Node Measurements

Hendrickx

Gevers

Bazanella

2019

IEEE Trans. Automat. Contr.

206

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“…Remember that known external signals r i are applied to each node, which we have not added on the figure for visibility reasons. Node i has three outgoing nodes, each of which has a vertex-disjoint directed path to the measured nodes 7, 8 and 9, namely the paths (1, 5, 7), (2,4,8) and (3,6,9); they are represented by dashed green arrows. As a result, the dotted red transfer functions G 1i , G 2i and G 3i can all be identified from these three measured nodes.…”

Section: Path-based Resultsmentioning

confidence: 99%

“…Proof of Theorem 4.1 1) The first part follows from the definition of a source and from the calculation of T from such G using (7). The second part follows from (9). The only way to identify the transfer function on an outgoing path from a source i is if an external input signal r i is applied at the source.…”

Section: Appendixmentioning

confidence: 99%

Identifiability of dynamical networks: Which nodes need be measured?

Bazanella

Gevers

Hendrickx

et al. 2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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Much recent research has dealt with the identifiability of a dynamical network in which the node signals are connected by causal linear time-invariant transfer functions and are possibly excited by known external excitation signals and/or unknown noise signals. So far all results on the identifiability of the whole network have assumed that all node signals are measured. Under this assumption, it has been shown that such networks are identifiable only if some prior knowledge is available about the structure of the network, in particular the structure of the excitation. In this paper we present the first results for the situation where not all node signals are measurable, under the assumptions that the topology of the network is known, that each node is excited by a known signal and that the nodes are noise-free. Using graph theoretical properties, we show that the transfer functions that can be identified depend essentially on the topology of the paths linking the corresponding vertices to the measured nodes. An important outcome of our research is that, under those assumptions, a network can often be identified using only a small subset of node measurements.

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“…The obtained indirect methods can address significantly more general settings than the existing network identification methods [17], [19], [21], [31], [42] which are typically limited to a specific measurement scheme, e.g., both the input and output are measured [17], [21], [31], [42]; or the input is unmeasured but the output is measured [19], [21].…”

Section: Indirect Identification Methodsmentioning

confidence: 99%

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

Shi¹,

Cheng²,

Hof³

2020

Preprint

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Identifiability of a single module in a network of transfer functions is determined by the question 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 work 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 identfiability conditions are satisfied, 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.

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Identification and Prediction in Dynamic Networks with Unobservable Nodes

Cited by 15 publications

References 11 publications

Identifiability of Dynamical Networks With Partial Node Measurements

Identifiability of Dynamical Networks With Partial Node Measurements

Identifiability of dynamical networks: Which nodes need be measured?

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

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