A priori identifiability: An overview on definitions and approaches

Anstett-Collin, Floriane; Denis-Vidal, Lilianne; Millérioux, Gilles

doi:10.1016/j.arcontrol.2020.10.006

Cited by 32 publications

(33 citation statements)

References 47 publications

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“…Then from the consistent block diagonal structures of the involved MVPs, straightforward algebraic manipulations show that U [iv,1] ⋆# (λ)U [1] (λ) ≡ Ir ⋆# and…”

Section: Appendix: Proof Of Some Technical Resultsmentioning

confidence: 99%

“…(A2), it is obvious that the satisfaction of Eq. (A6) is equivalent to the existence of a ryv × mz dimensional RFM Π2(λ), such that [1] yv (λ)Π2(λ) Substitute this relation back into Eq. (A5), the following equality is obtained,…”

Section: Appendix: Proof Of Some Technical Resultsmentioning

confidence: 99%

“…1,τ takes its maximum 1.7920 × 10 2 , which is far greater than the H ∞ norm of the TFM H(λ, Φ 1 (τ )) − H(λ, Φ 0 ) at other τ s. Fig. 4b shows the singular values of the frequency response of the associated H(λ, Φ [1] (τ )) − H(λ, Φ 0 ). Obviously, its condition number is quite large in the whole low frequency band, meaning that the associated external output differences are quite sensitive to the direction of an external input signal.…”

Section: [T ]mentioning

confidence: 96%

“…The latter has been attracting extensive research attentions for a long time in various fields, including engineering, finance, biology, etc. Nevertheless, it is still a challenging issue even for a lumped LTI system [1,8,9,14,21]. As structure information is widely recognized to be quite important in NDS analysis and synthesis, structure identifiability is used throughout this paper, in order to reflect this importance and to distinguish it from the traditional parameter identifiability, which is also adopted in other works, such as [13,14,16,17] and the references therein.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…3b and 4a is that there are some zigzags in their curves, which means that when the parameter τ or the stability margin increases monotonically and continuously, there may exist some abrupt and significant changes in NDS external output differences. Primary analyses show that this phenomenon is closely related to directionality of a multi-input multi-output system which is well known in systems and control theories [20,23], but its effects appear to have not been extensively studied in system identifications [1,9].…”

Section: [T ]mentioning

confidence: 99%

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Global Structure Identifiability and Reconstructibility of an NDS with Descriptor Subsystems

Zhou,

Yin

2021

Preprint

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This paper investigates requirements on a networked dynamic system (NDS) such that its subsystem interactions can be solely determined from experiment data or reconstructed from its overall model. The NDS is constituted from several subsystems whose dynamics are described through a descriptor form. Except regularity on each subsystem and the whole NDS, no other restrictions are put on either subsystem dynamics or subsystem interactions. A matrix rank based necessary and sufficient condition is derived for the global identifiability of subsystem interactions, which leads to several conclusions about NDS structure identifiability when there is some a priori information. This matrix also gives an explicit description for the set of subsystem interactions that can not be distinguished from experiment data only. In addition, under a well-posedness assumption, a necessary and sufficient condition is obtained for the reconstructibility of subsystem interactions from an NDS descriptor form model. This condition can be verified with each subsystem separately and is therefore attractive in the analysis and synthesis of a large-scale NDS. Simulation results show that rather than increases monotonically with the distance of subsystem interactions to the undifferentiable set, the magnitude of the external output differences between two NDSs with distinct subsystem interactions increases much more rapidly when one of them is close to be unstable. In addition, directions of probing signals are also very important in distinguishing external outputs of distinctive NDSs. These findings are expected to be helpful in identification experiment designs, etc.

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“…Then from the consistent block diagonal structures of the involved MVPs, straightforward algebraic manipulations show that U [iv,1] ⋆# (λ)U [1] (λ) ≡ Ir ⋆# and…”

Section: Appendix: Proof Of Some Technical Resultsmentioning

confidence: 99%

Section: Appendix: Proof Of Some Technical Resultsmentioning

confidence: 99%

Section: [T ]mentioning

confidence: 96%

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Section: [T ]mentioning

confidence: 99%

See 3 more Smart Citations

Global Structure Identifiability and Reconstructibility of an NDS with Descriptor Subsystems

Zhou,

Yin

2021

Preprint

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Moving Horizon Parameter Estimation for an Enzyme‐Catalyzed Transamination Reaction with Integrated Product Removal

Behrens,

Tiedemann,

Kunde

et al. 2024

Chemie Ingenieur Technik

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Chiral amines are key building blocks in producing active pharmaceutical ingredients and can be synthesized via the amine transaminase pathway under mild conditions with eco‐friendly solvents. For model‐based design and control, mathematical models can be utilized. This requires reliable parameterization of the model. In this study, a model for the production of (S)‐(3 methoxyphenyl)‐ethylamine is presented. Parameter identifiability is analyzed using the method of profile likelihoods. The parameter identifiability is then tested in two different batch operation scenarios by using moving horizon estimation, which can be applied for on‐line model adaption and control purposes. In a batch process, identifiability decreases over time. A repetitive batch strategy improves parameter identifiability.

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On Parameter Identifiability in Network-Based Epidemic Models

Kiss

Šimon

2023

Bull Math Biol

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Modelling epidemics on networks represents an important departure from classical compartmental models which assume random mixing. However, the resulting models are high-dimensional and their analysis is often out of reach. It turns out that mean-field models, low-dimensional systems of differential equations, whose variables are carefully chosen expected quantities from the exact model provide a good approximation and incorporate explicitly some network properties. Despite the emergence of such mean-field models, there has been limited work on investigating whether these can be used for inference purposes. In this paper, we consider network-based mean-field models and explore the problem of parameter identifiability when observations about an epidemic are available. Making use of the analytical tractability of most network-based mean-field models, e.g. explicit analytical expressions for leading eigenvalue and final epidemic size, we set up the parameter identifiability problem as finding the solution or solutions of a system of coupled equations. More precisely, subject to observing/measuring growth rate and final epidemic size, we seek to identify parameter values leading to these measurements. We are particularly concerned with disentangling transmission rate from the network density. To do this, we give a condition for practical identifiability and we find that except for the simplest model, parameters cannot be uniquely determined, that is, they are practically unidentifiable. This means that there exist multiple solutions (a manifold of infinite measure) which give rise to model output that is close to the data. Identifying, formalising and analytically describing this problem should lead to a better appreciation of the complexity involved in fitting models with many parameters to data.

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A priori identifiability: An overview on definitions and approaches

Cited by 32 publications

References 47 publications

Global Structure Identifiability and Reconstructibility of an NDS with Descriptor Subsystems

Global Structure Identifiability and Reconstructibility of an NDS with Descriptor Subsystems

Moving Horizon Parameter Estimation for an Enzyme‐Catalyzed Transamination Reaction with Integrated Product Removal

On Parameter Identifiability in Network-Based Epidemic Models

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