Observability of Network Systems: A Critical Review of Recent Results

Montanari, Arthur N.; Aguirre, Luís A.

doi:10.1007/s40313-020-00633-5

Cited by 20 publications

(8 citation statements)

References 128 publications

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“…A sufficient condition for this latter assumption is that every target node has a self-link. The importance of including self-links in dynamical networks models, especially for state control and estimation applications, has been thoroughly discussed in the literature ( 7 , 45 , 46 ). Indeed, dilations are not found in a broad range of dynamical networks, including diffusively coupled systems.…”

Section: Resultsmentioning

confidence: 99%

“…The deception attack tampers with the transmitted measurement φa(t) from the highlighted PMU (red circle). The inset illustrates the inference graph of the dynamical system ( 6)- (7), where each generator bus (vertex) is represented by two state nodes (phase φi and frequency φi in ( 6)) and each generator terminal and load bus is represented by a single state node (phase φi in ( 7)). Links with state nodes outside the highlighted neighborhood are omitted.…”

Section: Resultsmentioning

confidence: 99%

“…In particular, observability constitutes the necessary and sufficient condition that guarantees the existence and enables the design of full-state estimators—such as Luenberger observers ( 3 ) and Kalman filters ( 4 ). Despite the success of state observers in uncountable engineering applications, high dimensionality is still an obstacle to the direct use of these methods in large-scale dynamical networks ( 5 – 7 ). This calls for different approaches and novel techniques ( 8 – 14 ) to overcome the lack of scalability of existing methods.…”

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confidence: 99%

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Functional observability and target state estimation in large-scale networks

Montanari

Duan

Aguirre

et al. 2021

Proc. Natl. Acad. Sci. U.S.A.

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The quantitative understanding and precise control of complex dynamical systems can only be achieved by observing their internal states via measurement and/or estimation. In large-scale dynamical networks, it is often difficult or physically impossible to have enough sensor nodes to make the system fully observable. Even if the system is in principle observable, high dimensionality poses fundamental limits on the computational tractability and performance of a full-state observer. To overcome the curse of dimensionality, we instead require the system to be functionally observable, meaning that a targeted subset of state variables can be reconstructed from the available measurements. Here, we develop a graph-based theory of functional observability, which leads to highly scalable algorithms to 1) determine the minimal set of required sensors and 2) design the corresponding state observer of minimum order. Compared with the full-state observer, the proposed functional observer achieves the same estimation quality with substantially less sensing and fewer computational resources, making it suitable for large-scale networks. We apply the proposed methods to the detection of cyberattacks in power grids from limited phase measurement data and the inference of the prevalence rate of infection during an epidemic under limited testing conditions. The applications demonstrate that the functional observer can significantly scale up our ability to explore otherwise inaccessible dynamical processes on complex networks.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

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Functional observability and target state estimation in large-scale networks

Montanari

Duan

Aguirre

et al. 2021

Proc. Natl. Acad. Sci. U.S.A.

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“…including neuronal models [29,30], metabolic reactions [31], ecological systems [32], and networks [33][34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Functional observability and subspace reconstruction in nonlinear systems

Montanari

Freitas

Proverbio

2022

Phys. Rev. Research

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Time-series analysis is fundamental for modeling and predicting dynamical behaviors from timeordered data, with applications in many disciplines such as physics, biology, finance, and engineering. Measured time-series data, however, are often low dimensional or even univariate, thus requiring embedding methods to reconstruct the original system's state space. The observability of a system establishes fundamental conditions under which such reconstruction is possible. However, complete observability is too restrictive in applications where reconstructing the entire state space is not necessary and only a specific subspace is relevant. Here, we establish the theoretic condition to reconstruct a nonlinear functional of state variables from measurement processes, generalizing the concept of functional observability to nonlinear systems. When the functional observability condition holds, we show how to construct a map from the embedding space to the desired functional of state variables, characterizing the quality of such reconstruction. The theoretical results are then illustrated numerically using chaotic systems with contrasting observability properties. By exploring the presence of functionally unobservable regions in embedded attractors, we also apply our theory for the early warning of seizure-like events in simulated and empirical data. The studies demonstrate that the proposed functional observability condition can be assessed a priori to guide time-series analysis and experimental design for the dynamical characterization of complex systems.

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“…12 Consequently, a graphtheoretical perspective of observability, as developed by Lin, 13 has been presented to tackle networks of linear systems. [14][15][16][17][18] The graph is in fact a fluence graph, as introduced by Mason, 19 which encodes the dependencies (links) between the state variables (nodes). From the structure of this graph in terms of the root strongly connected components, 14 it is possible to obtain a minimum set of variables (sensors) that render the network observable.…”

Section: Introductionmentioning

confidence: 99%

Observability analysis and observer design of networks of Rössler systems

Sendiña‐Nadal¹,

Letellier²

2022

Preprint

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We address the problem of retrieving the full state of a network of Rössler systems from the knowledge of the actual state of a limited set of nodes. The selection of the nodes where sensors are placed is carried out in a hierarchical way through a procedure based on graphical and symbolic observability approaches. By using a map directly obtained from the governing equations, we design a nonlinear network observer which is able to unfold the state of the non measured nodes with minimal error. For sparse networks, the number of sensors scales with half the network size and node reconstruction errors are lower in networks with heterogeneous degree distributions. The method performs well even in the presence of parameter mismatch and non-coherent dynamics and, therefore, we expect it to be useful for designing robust network control laws.

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Observability of Network Systems: A Critical Review of Recent Results

Cited by 20 publications

References 128 publications

Functional observability and target state estimation in large-scale networks

Functional observability and target state estimation in large-scale networks

Functional observability and subspace reconstruction in nonlinear systems

Observability analysis and observer design of networks of Rössler systems

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