Identifiability of Dynamical Networks With Singular Noise Spectra

Gevers, Michel; Bazanella, Alexandre Sanfelice; Pimentel, Guilherme Araujo

doi:10.1109/tac.2018.2866448

Cited by 14 publications

(8 citation statements)

References 8 publications

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“…For the sequel, it is important to note that this covariance matrix (as any other positive semidefinite matrix) can be decomposed as Σ 0,V = Ξ 0,V Ξ T 0,V where Ξ 0,V is a matrix with n V rows and a number of columns equal to the rank of Σ 0,V (see e.g. [11]).…”

Section: Network Descriptionmentioning

confidence: 99%

“…However, until now, even though some preliminary results can be found in e.g., [8,13,9], data informativity for dynamic network identification has only been briefly touched upon in the literature. As opposed to data informativity, the concept of network identifiability has been extensively explored (see e.g., [15,11,16,23,5,20]). In a nutshell, a network is said identifiable if we can uniquely retrieve (part of) the open-loop representation of the network (i.e., Ḡ0 (z)) from closed-loop representations of the network (i.e., representations of the tranfer between the exogenous signals and (some of) the node signals).…”

Section: Introductionmentioning

confidence: 99%

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On the informativity of direct identification experiments in dynamical networks

Bombois¹,

Colin²,

Hof³

et al. 2023

Automatica

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Section: Network Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the informativity of direct identification experiments in dynamical networks

Bombois¹,

Colin²,

Hof³

et al. 2023

Automatica

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“…where e(t) is vector of white noises with covariance matrix Λ; H(q) is proper and stable. Depending on the chosen spectral factorization of Φ v , Λ may have dimension L or p [26], [36].…”

Section: A Dynamic Networkmentioning

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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“…For identification methods to provide consistent estimates of some modules it is necessary that they can be uniquely determined from the network data -that is, that the modules are identifiable. The question of whether some modules, or the full network, are identifiable has been explored in Gevers & Bazanella (2015); Weerts et al (2015); Gevers et al (2017); Bazanella et al (2017) and for the rank-reduced noise case in Weerts et al (2018b); Gevers et al (2019). Identifiability of the modules is determined primarily by the location of excitations and measurements in the network.…”

Section: Introductionmentioning

confidence: 99%

Optimal excitation and measurement pattern for cascade networks

Mapurunga¹,

Bazanella²

2021

Preprint

Self Cite

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This work deals with accuracy analysis of dynamical systems interconnected in a cascade structure. For a cascade network there are a number of experimental settings for which the dynamic systems within the network can be identified. We study the problem of choosing which excitation and measurement pattern delivers the most accurate parameter estimates for the whole network. The optimal experiment is based on the accuracy assessed through the asymptotic covariance matrix of the prediction error method, while the cost criterion is the number of excitations and measurements. We develop theoretical results under the assumptions that all dynamic systems are equal and with equal signal-to-noise ratio throughout the network. We show that there are experimental settings which result in equal overall precision and that there is an excitation and measurement pattern that yields more accurate results than others. From these results a guideline based on the topology of the network emerges for the choice of the experimental setting. We provide numerical results which attest that the principles behind this guideline are also valid for more general situations.

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Identifiability of Dynamical Networks With Singular Noise Spectra

Cited by 14 publications

References 8 publications

On the informativity of direct identification experiments in dynamical networks

On the informativity of direct identification experiments in dynamical networks

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

Optimal excitation and measurement pattern for cascade networks

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