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Graph Laplacian based matrix design for finitetime distributed average consensus
 IN: PROC. AMERICAN CONTR. CONF
, 2012
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Decentralized Laplacian eigenvalues estimation and collaborative network topology identification
 In the 3rd IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys’12
, 2012
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 9 (5 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Distributed Computation of Tensor Decompositions
 in Collaborative Networks,” Proc. IEEE CAMSAP 2013, SaintMartin
, 2013
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 3 (2 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Distributed Design of Finitetime Average Consensus Protocols
 IFAC WORKSHOP ON DISTRIBUTED ESTIMATION AND CONTROL (NECSYS 2013), KOBLENZ: GERMANY (2013)
, 2013
"... In this paper, we are interested in the finitetime average consensus problem for multiagent systems or wireless sensor networks. This issue is formulated in a discretetime framework by utilizing a linear iteration scheme, where each node repeatedly updates its value as a weighted linear combinati ..."
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Cited by 1 (0 self)
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In this paper, we are interested in the finitetime average consensus problem for multiagent systems or wireless sensor networks. This issue is formulated in a discretetime framework by utilizing a linear iteration scheme, where each node repeatedly updates its value as a weighted linear combination of its own value and those of its neighbors. Unlike most of research in literature, this work deals with the foremost step, called configuration step, during which the consensus protocol is to be set up in each agent. Designing consensus protocols can be viewed as a matrix factorization problem. For connected undirected graphs, we propose a learning method for solving such matrix factorization problem in a distributed way. More precisely, we first show how solving this problem for the particular case of strongly regular graphs. Then, a distributed gradient backpropagation algorithm is derived for the general case. The performance of the proposed algorithm is evaluated by means of simulation results.
Distributed Estimation of Graph Laplacian Eigenvalues by the Alternating Direction of Multipliers Method
"... Abstract: This paper presents a new method for estimating the eigenvalues of the Laplacian matrix associated with the graph describing the network topology of a multiagent system. Given an approximate value of the average of the initial condition of the network state and some intermediate values o ..."
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Abstract: This paper presents a new method for estimating the eigenvalues of the Laplacian matrix associated with the graph describing the network topology of a multiagent system. Given an approximate value of the average of the initial condition of the network state and some intermediate values of the network state when performing a Laplacianbased average consensus, the estimation of the Laplacian eigenvalues is obtained by solving the factorization of the averaging matrix. For this purpose, in contrast to the state of the art, we formulate a convex optimization problem that is solved in a distributed way by means of the Alternating Direction Method of Multipliers (ADMM). The main variables in the optimization problem are the coefficients of a polynomial whose roots are precisely the inverse of the distinct nonzero Laplacian eigenvalues. The performance of the proposed method is evaluated by means of simulation results.
Grenoble RhôneAlpes THEME Modeling, Optimization, and Control of Dynamic SystemsTable of contents
"... 3.1. Dynamic nonregular systems 2 3.2. Nonsmooth optimization 3 ..."
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Decentralized Laplacian Eigenvalues Estimation and Collaborative Network Topology Identification
, 2012
"... Abstract: 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 KhatriRao product of matrices. Then we consider the problem of esti ..."
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Abstract: 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 KhatriRao 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 finitetime, 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 consensusbased least squares method.
1Accelerating Consensus by Spectral Clustering and Polynomial Filters
"... Abstract—It is known that polynomial filtering can accelerate the convergence towards average consensus on an undirected network. In this paper the gain of a secondorder filtering is investigated. A set of graphs is determined for which consensus can be attained in finite time, and a preconditioner ..."
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Abstract—It is known that polynomial filtering can accelerate the convergence towards average consensus on an undirected network. In this paper the gain of a secondorder filtering is investigated. A set of graphs is determined for which consensus can be attained in finite time, and a preconditioner is proposed to adapt the undirected weights of any given graph to achieve fastest convergence with the polynomial filter. The corresponding cost function differs from the traditional spectral gap, as it favors grouping the eigenvalues in two clusters. A possible loss of robustness of the polynomial filter is also highlighted. I. CONSENSUS ACCELERATION S INCE their introduction in [1], (discretetime) consensusalgorithms have attracted almost as much attention as their dual, fast mixing Markov chains [2], [3]. Improving the convergence speed of this basic building block for e.g. distributed computation and sensor fusion has been a major focus. For synchronized fixed networks, one can optimize the weights on the links [2], add local memory [4], or introduce timevarying filters [5], [6]. The present paper establishes the benefit of combining polynomial filtering with optimization of link weights. Consider an undirected and connected graph G(V, E) with N nodes ∈ V and M edges ∈ E. Denote the node states as x = (x1, x2,..., xN) ∈ RN. The basic linear consensus dynamics on G is xi(k+1) = xi(k) + w