Dynamic network structure identification with prediction error methods - basic examples

Dankers, Arne; Hof, Paul M.J. Van den; Heuberger, P.S.C.; Bombois, Xavier

doi:10.3182/20120711-3-be-2027.00263

Cited by 19 publications

(22 citation statements)

References 22 publications

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“…We shall define this new notion of generic identifiability of the network in precise terms in Section V. In order to give the reader an intuitive feeling for this notion, we illustrate it with the following example. 3 Example 1: Consider a network whose topology is defined by the following network matrix:…”

Section: Standing Assumptionsmentioning

confidence: 99%

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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: Standing Assumptionsmentioning

confidence: 99%

“…Finally, in the network of Figure 3, all 5 transfer functions can be identified by measuring just two nodes: either nodes 1 AND 2, OR nodes 1 AND 3. 3 Starting in this example and for the remaining of the paper, we omit the dependence on q whenever it creates no confusion.…”

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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“…Note thatJ = ∅ and there is no self-loop at k. Thus, Q (f ) kj = Q kj . It follows in a similar manner that: By replacing (28) in (27) and the resulting expression into (26) we obtain the assertion using the matrix inversion lemma.…”

Section: Identification Of Individual Transfer Functions In a Ldimentioning

confidence: 89%

“…In the last decade several network models have emerged, such as Dynamical Structural Function (DSF) models [9], Linear Dynamic Graphs (LDGs) [26], [13] and the dynamic interconnection proposed in [27]. These models share very similar characteristics, the main one being that they can be interpreted via graphs in a way analogous to Signal Flow Graphs [28].…”

Section: Graphical Representationsmentioning

confidence: 99%

Signal Selection for Estimation and Identification in Networks of Dynamic Systems: A Graphical Model Approach

Materassi

Salapaka

2020

IEEE Trans. Automat. Contr.

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Network systems have become a ubiquitous modeling tool in many areas of science where nodes in a graph represent distributed processes and edges between nodes represent a form of dynamic coupling. When a network topology is already known (or partially known), two associated goals are (i) to derive estimators for nodes of the network which cannot be directly observed or are impractical to measure; and (ii) to quantitatively identify the dynamic relations between nodes. In this article we address both problems in the challenging scenario where only some outputs of the network are being measured and the inputs are not accessible. The approach makes use of the notion of d-separation for the graph associated with the network. In the considered class of networks, it is shown that the proposed technique can determine or guide the choice of optimal sparse estimators. The article also derives identification methods that are applicable to cases where loops are present providing a different perspective on the problem of closed-loop identification. The notion of d-separation is a central concept in the area of probabilistic graphical models, thus an additional contribution is to create connections between control theory and machine learning techniques.

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“…in drugs discovery [9]. Questions such as those of understanding under which conditions the connection structure of the individual subsystems can be identified [10], or how to deal with structure identification for uncertain general complex dynamical networks with time delay [11] have been addressed within some interesting frameworks.…”

Section: Introductionmentioning

confidence: 99%

Identification of distributed systems with logical interaction structure

Martini

Fagiolini

Giarré

et al. 2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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This paper focuses on the structure identification problem for a class of networked systems, where the interaction among components or agents is described through logical maps. In particular, agents are heterogeneous cooperating systems, i.e. they may have different individual dynamics and different interaction rules depending on input events. While we assume that the individual agents' dynamics are known, each agent has partial knowledge of the logical map encoding the interaction of another agent with its neighbors. Based on the so-called algebraic normal form for binary functions, we present a technique by which the network structure described by a logical function can be dynamically estimated as its truth table is observed. The estimated map is a lower approximation of the real one, which coincides with it as soon as the truth table is entirely observed. Application of the proposed technique to a real system, where agents are mobile robots whose motion depends on logical conditions on their neighborhood, is finally presented.

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Dynamic network structure identification with prediction error methods - basic examples

Cited by 19 publications

References 22 publications

Identifiability of Dynamical Networks With Partial Node Measurements

Identifiability of Dynamical Networks With Partial Node Measurements

Signal Selection for Estimation and Identification in Networks of Dynamic Systems: A Graphical Model Approach

Identification of distributed systems with logical interaction structure

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