A Distributed Solution to the Network Reconstruction Problem

International audienceIt has been recently shown in Ren et al. (2010) that by collecting noise-contaminated time series generated by a coupled-oscillator system at each node of a network, it is possible to robustly reconstruct its topology, i.e. determine the graph Laplacian. Restricting ourselves to linear consensus dynamics over undirected communication networks, in this paper we introduce a new dynamic average consensus least-squares algorithm to locally estimate these time series at each node, thus making the reconstruction process fully distributed and more easily applicable in the real world. We also propose a novel efficient method for separating the off-diagonal entries of the reconstructed Laplacian, and examine several concepts related to the trace of the dynamic correlation matrix of the coupled single integrators, which is a distinctive element of our network reconstruction method. The theory is illustrated with examples from computer, power and transportation systems

Distributed network topology reconstruction in presence of anonymous nodes

International audienceThis paper concerns the problem of reconstructing the network topology from data propagated through the network by means of an average consensus protocol. The proposed method is based on the distributed estimation of graph Lapla-cian spectral properties. Precisely, the identification of the network topology is implemented by estimating both eigen-values and eigenvectors of the consensus matrix, which is related to the graph Laplacian matrix. In this paper, we focus the exposition on the estimation of the eigenvectors since the eigenvalues estimation can be achieved based on recent results of the literature using the same kind of data. We show how the topology can be reconstructed in presence of anonymous nodes, i.e. nodes that do not disclose their ID

Distributed Computation of Tensor Decompositions in Collaborative Networks

International audienceIn this paper, we consider the issue of distributed computation of tensor decompositions. A central unit observing a global data tensor assigns different data sub-tensors to several computing nodes grouped into clusters. The goal is to distribute the computation of a tensor decomposition across the different computing nodes of the network, which is particularly useful when dealing with large-scale data tensors. However, this is only possible when the data sub-tensors assigned to each computing node in a cluster satisfies minimum conditions for uniqueness. By allowing collaboration between computing nodes in a cluster, we show that average consensus based estimation is useful to yield unique estimates of the factor matrices of each data sub-tensor. Moreover, an essentially unique reconstruction of the global factor matrices at the central unit is possible by allowing the subtensors assigned to different clusters to overlap in one mode. The proposed approach may be useful to a number of distributed tensor-based estimation problems in signal processing

Distributed Computation of Tensor Decompositions in Collaborative Networks

International audienceIn this paper, we consider the issue of distributed computation of tensor decompositions. A central unit observing a global data tensor assigns different data sub-tensors to several computing nodes grouped into clusters. The goal is to distribute the computation of a tensor decomposition across the different computing nodes of the network, which is particularly useful when dealing with large-scale data tensors. However, this is only possible when the data sub-tensors assigned to each computing node in a cluster satisfies minimum conditions for uniqueness. By allowing collaboration between computing nodes in a cluster, we show that average consensus based estimation is useful to yield unique estimates of the factor matrices of each data sub-tensor. Moreover, an essentially unique reconstruction of the global factor matrices at the central unit is possible by allowing the subtensors assigned to different clusters to overlap in one mode. The proposed approach may be useful to a number of distributed tensor-based estimation problems in signal processing

Observability in Connected Strongly Regular Graphs and Distance Regular Graphs

International audienceThis paper concerns the study of observability in consensus networks modeled with strongly regular graphs or distance regular graphs. We first give 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 define some bipartite graphs that capture the observability properties of the graph to be studied. In particular, we show that necessary and sufficient observability conditions are given by the nullity of the so-called local bipartite observability graph (resp. local unfolded bipartite observability graph) for strongly regular graphs (resp. distance regular graphs). When the nullity cannot be derived directly from the structure of these bipartite graphs, the rank of the associated bi-adjacency matrix allows evaluating observability. Eventually, as a by-product of the main results we show that non-observability can be stated just by comparing the valency of the graph to be studied with a bound computed from the number of vertices of the graph and its diameter. Similarly nonobservability can also be stated by evaluating the size of the maximum matching in the above mentioned bipartite graphs

Distributed Estimation of Graph Laplacian Eigenvalues by the Alternating Direction of Multipliers Method

International audienceThis paper presents a new method for estimating the eigenvalues of the Laplacian matrix associated with the graph describing the network topology of a multi-agent 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 Laplacian-based 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

Contributions à l’analyse des systèmes en réseau

La dernière décennie a vu l’émergence des travaux autour des systèmes dynamiques interconnectés (systèmes en réseaux ou systèmes cyberphysiques). Dans cette habilitation à diriger des recherches, je donne un aperçu des contributions qui ont été les miennes durant la dernière décennie sur : l’analyse des systèmes en réseaux (problème de consensus, observabilité et application à la préservation de la vie privée), le traitement des données de grandes dimensions (analyse tensorielle pour l’identification des systèmes non-linéaires, décomposition distribuée de tenseurs de grandes dimensions), et l’application à la mobilité intelligente (navigation en milieu urbain, prédiction et estimation de trafic, estimation d’attitude pour la navigation pédestre). Une prospective est ensuite développée autour de la sécurité des systèmes en réseaux, en se basant sur la théorie des systèmes, et sur l’analyse des données de grandes dimensions organisées dans des tenseurs de données avec des applications sur la mobilité intelligente

Graph Laplacian based Matrix Design for Finite-Time Distributed Average Consensus

International audienceIn this paper, we consider the problem of finding a linear iteration scheme that yields distributed average consensus in a finite number of steps D. By modeling interactions between the nodes in the network by means of a time-invariant undirected graph, the problem is solved by deriving a set of D Laplacian based consensus matrices. We show that the number of steps is given by the number of nonzero distinct eigenvalues of the graph Laplacian matrix. Moreover the inverse of these eigenvalues constitute the step-sizes of the involved Laplacian based consensus matrices. When communications are made through an additive white Gaussian noise channel, based on an ensemble averaging method, we show how average consensus can be asymptotically reached. Performance analysis of the suggested protocol is given along with comparisons with other methods in the literature

Adaptive Kalman Filter for MEMS-IMU based Attitude Estimation under External Acceleration and Parsimonious use of Gyroscopes

International audienceThis paper presents a viable quaternion-based Adaptive Kalman Filter (q-AKF) that is designed for rigid body attitude estimation. This approach is an alternative to overcome the limitations of the classical Kalman filter. The q-AKF processes data from a small inertial/magnetic sensor module containing triaxial gyroscopes, accelerometers, and magnetometers. The proposed approach addresses two challenges. The first one concerns attitude estimation during various dynamic conditions, in which external acceleration occurs. Although external acceleration is one of the main source of loss of performance in attitude estimation methods, this problem has not been sufficiently addressed in the literature. An adaptive algorithm compensating external acceleration from the residual in the accelerometer is proposed. At each step, the covariance matrix associated with the external acceleration is estimated to adaptively tune the filter gain. The second challenge is focused on the energy consumption issue of gyroscopes for long-term battery life of Inertial Measurement Units. We study the way to reduce the gyro measurement acquisition while maintaining acceptable attitude estimation. Through numerical simulations, under external acceleration and parsimonious gyroscope's use, the efficiency of the proposed q-AKF is illustrated