Dynamic Networks: Representations, Abstractions, and Well-Posedness

Woodbury, Nathan; Dankers, Arne; Warnick, Sean

doi:10.1109/cdc.2018.8619098

Cited by 3 publications

(6 citation statements)

References 27 publications

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“…2) j = o and i ∈ Q. From (30), we have Ḡji = (I − G jj ) −1 G ji where G jj and G ji are given by ( 25), leading to (41).…”

Section: Appendix B Proof Of Theoremmentioning

confidence: 99%

“…Therefore, for this case, G jj = G jj and G ji = G ji , which are given by (24). This leads to (41). Lemma 3: Consider a dynamic network as defined in (15) where the nonmeasured node signals w Z are immersed, and let U be decomposed in sets A and B satisfying condition 2.…”

Section: Appendix B Proof Of Theoremmentioning

confidence: 99%

“…Under the parallel path and loop condition 1, the second terms on the right-hand sides of (49), (50) are zero, so that Gji = G ji and Gjj = 0. What remains to be shown is that in (41) implying that columns in this matrix related to inputs k ∈ A are zero.…”

Section: Appendix B Proof Of Theoremmentioning

confidence: 99%

“…Proof: We will show that Ḡki is strictly proper if all paths from w i to w k have a delay. For any k ∈ Y, i ∈ D, Ḡki is given by either (41) or (42) with j = k. The situation that is not covered by ( 41), (42) is the case where i = {o}, but from (34), it follows that Ḡko = 0, for k ∈ Y. So for this situation strictly properness is guaranteed.…”

Section: Appendix C Proof Of Theoremmentioning

confidence: 99%

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A Local Direct Method for Module Identification in Dynamic Networks With Correlated Noise

Ramaswamy

Hof

2021

IEEE Trans. Automat. Contr.

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“…2) j = o and i ∈ Q. From (30), we have Ḡji = (I − G jj ) −1 G ji where G jj and G ji are given by ( 25), leading to (41).…”

Section: Appendix B Proof Of Theoremmentioning

confidence: 99%

Section: Appendix B Proof Of Theoremmentioning

confidence: 99%

Section: Appendix B Proof Of Theoremmentioning

confidence: 99%

Section: Appendix C Proof Of Theoremmentioning

confidence: 99%

See 2 more Smart Citations

A Local Direct Method for Module Identification in Dynamic Networks With Correlated Noise

Ramaswamy

Hof

2021

IEEE Trans. Automat. Contr.

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“…This is the reason behind the distinct notions of well-posedness and causal well-posedness in Definition 13. For a more extensive discussion on the well-posedness of DSF structure we refer to [30] Definition 14 (Graphical representations of a LDIM and its associated perfect directed graph (PDG)). Given a LDIM, (Q(z), e), with output processes y = (y T 1 |...|y T n ) T and a directed graph G = (V, E) where V = {y 1 , ..., y n } we say that G is a graphical representation of the LDIM if…”

Section: Linear Dynamic Influence Models and Their Graphical Represen...mentioning

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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Controlling Diffusive Network Dynamics using a Stochastically-Mobile Sensor-Actuator Platform

2019

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Dynamic Networks: Representations, Abstractions, and Well-Posedness

Cited by 3 publications

References 27 publications

A Local Direct Method for Module Identification in Dynamic Networks With Correlated Noise

A Local Direct Method for Module Identification in Dynamic Networks With Correlated Noise

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

Controlling Diffusive Network Dynamics using a Stochastically-Mobile Sensor-Actuator Platform

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