Observability and estimation in distributed sensor networks

Ji, Meng; Egerstedt, Magnus

doi:10.1109/cdc.2007.4434659

Cited by 39 publications

(38 citation statements)

References 20 publications

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“…As observed by [10], we can always check the rank condition to determine the observability of the network. However, it becomes infeasible when the number of nodes becomes very large.…”

Section: A Problem Formulationmentioning

confidence: 99%

“…controllability) [7], [8], [9]. Then, resorting to the notion of equitable partitions of a graph necessary conditions have been stated in [10] for observability over arbitrary graphs and in [7], [8], [11], [12] for controllability. Unfortunately, these conditions are not sufficient except for certain classes of systems (chain and multichain graphs with a single leader at the extremity of the chain [12]).…”

Section: Introductionmentioning

confidence: 99%

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Algebraic characterization of observability in distance-regular consensus networks

Kibangou

Commault

2013

52nd IEEE Conference on Decision and Control

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Abstract-In this paper, we study the observability issue in consensus networks modeled with strongly regular graphs or distance regular graphs. We derive a Kalman-like simple algebraic criterion for observability in distance regular graphs. This criterion consists in evaluating the rank of a matrix built with the components of the Bose-Mesner algebra associated with the considered graph. Then, we state a simple necessary condition of observability based on parameters of the graph, namely the diameter, the degree, and the number of vertices of the graph.

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“…As observed by [10], we can always check the rank condition to determine the observability of the network. However, it becomes infeasible when the number of nodes becomes very large.…”

Section: A Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Algebraic characterization of observability in distance-regular consensus networks

Kibangou

Commault

2013

52nd IEEE Conference on Decision and Control

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“…Other contributions on the controllability of network systems can be found in [8], [9], [10]. Observability has been studied for the first time in [11], where necessary conditions for observability, as in the dual reachability setting investigated in [5] and [6], were provided. A parallel research line investigates a slightly different property called structural observability [12].…”

Section: Introductionmentioning

confidence: 99%

Observability and reachability of grid graphs via reduction and symmetries

Notarstefano

Parlangeli

2011

IEEE Conference on Decision and Control and European Control Conference

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In this paper we investigate the observability and reachability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a grid. More in detail, we characterize the structure of the grid eigenvectors by means of suitable decompositions of the graph. For each eigenvalue, based on its multiplicity and on suitable symmetries of the corresponding eigenvectors, we provide necessary and sufficient conditions to characterize all and only the nodes from which the network system is observable (reachable). We discuss the proposed criteria and show, through suitable examples, how such criteria reduce the complexity of the observability (respectively reachability) analysis of the grid.

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“…The observability of networks, and consensus networks in particular, is the topic of several recent contributions. In Ji and Egerstedt (2007), necessary conditions for observability are derived based on equitable partitions of a graph and the interlacing theory. More recently, in Parlangeli and Notarstefano (2012), necessary and sufficient conditions have been provided for path and cycle graphs.…”

Section: Introductionmentioning

confidence: 99%

Decentralized Laplacian Eigenvalues Estimation and Collaborative Network Topology Identification

Kibangou

Commault

2012

IFAC Proceedings Volumes

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In this paper we first study observability conditions on networks. Based on spectral properties of graphs, we state new sufficient or necessary conditions for observability. These conditions are based on properties of the Khatri-Rao product of matrices. Then we consider the problem of estimating the eigenvalues of the Laplacian matrix associated with the graph modeling the interconnections between the nodes of a given network. Eventually, we extend the study to the identification of the network topology by estimating both eigenvalues and eigenvectors of the network matrix. In addition, we show how computing, in finite-time, some linear functionals of the state initial condition, including average consensus. Specifically, based on properties of the observability matrix, we show that Laplacian eigenvalues can be recovered by solving a local eigenvalue decomposition on an appropriately constructed matrix of observed data. Unlike FFT based methods recently proposed in the literature, in the approach considered herein, we are also able to estimate the multiplicities of the eigenvalues. Then, for identifying the network topology, the eigenvectors are estimated by means of a consensus-based least squares method.

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Observability and estimation in distributed sensor networks

Cited by 39 publications

References 20 publications

Algebraic characterization of observability in distance-regular consensus networks

Algebraic characterization of observability in distance-regular consensus networks

Observability and reachability of grid graphs via reduction and symmetries

Decentralized Laplacian Eigenvalues Estimation and Collaborative Network Topology Identification

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