Convergence Speed in Distributed Consensus and Averaging

Olshevsky, Alex; Tsitsiklis, John N.

doi:10.1137/110837462

Cited by 196 publications

(184 citation statements)

References 41 publications

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“…In addition to providing insight into the synchronization of nonlinear systems, we note that Eq. (2.2) has many applications itself including consensus algorithms for sensor networks [35, 48, 37], where it is often assumed that ω n = ω for each n .…”

Section: Oscillator Models For Phase Synchronizationmentioning

confidence: 99%

“…The power grid, for example, must provide electricity following regional specifications (e.g., alternating current at 120 volts and 60 hertz in the United States) and a breakdown of synchronization can lead to costly blackouts [38, 50, 59, 31]. Other technologies in which synchronization plays a crucial role include Josephson junctions circuits [64, 46], physical infrastructure [57], electro-chemical oscillators [23], synthetic biological oscillators [41], and distributed sensor networks [35, 48, 37, 36]. Synchronization is also ubiquitous in biological systems [66], where applications include coordinated neuronal activity in the brain [28, 49], cardiac rhythms of the heart [30, 22], circadian rhythms governing sleep cycles [47], gene regulation [26], and intestinal activity [15, 2].…”

Section: Introductionmentioning

confidence: 99%

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Synchronization of Heterogeneous Oscillators Under Network Modifications: Perturbation and Optimization of the Synchrony Alignment Function

Taylor¹,

Skardal

Sun

2016

SIAM J. Appl. Math.

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Synchronization is central to many complex systems in engineering physics (e.g., the power-grid, Josephson junction circuits, and electro-chemical oscillators) and biology (e.g., neuronal, circadian, and cardiac rhythms). Despite these widespread applications—for which proper functionality depends sensitively on the extent of synchronization—there remains a lack of understanding for how systems can best evolve and adapt to enhance or inhibit synchronization. We study how network modifications affect the synchronization properties of network-coupled dynamical systems that have heterogeneous node dynamics (e.g., phase oscillators with non-identical frequencies), which is often the case for real-world systems. Our approach relies on a synchrony alignment function (SAF) that quantifies the interplay between heterogeneity of the network and of the oscillators and provides an objective measure for a system’s ability to synchronize. We conduct a spectral perturbation analysis of the SAF for structural network modifications including the addition and removal of edges, which subsequently ranks the edges according to their importance to synchronization. Based on this analysis, we develop gradient-descent algorithms to efficiently solve optimization problems that aim to maximize phase synchronization via network modifications. We support these and other results with numerical experiments.

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Section: Oscillator Models For Phase Synchronizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Synchronization of Heterogeneous Oscillators Under Network Modifications: Perturbation and Optimization of the Synchrony Alignment Function

Taylor¹,

Skardal

Sun

2016

SIAM J. Appl. Math.

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“…It is well-known that the algebraic connectivity of a network, the smallest non-zero eigenvalue of the network Laplacian matrix, characterizes the convergence speed of the average-consensus algorithm [23], [24]. Therefore, our goal is to identify the most critical node whose removal causes the largest descent in algebraic connectivity which we call as the algebraic connectivity descent.…”

Section: Introductionmentioning

confidence: 99%

Distributed Identification of the Most Critical Node for Average Consensus

Líu

Cao

et al. 2015

IEEE Trans. Signal Process.

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In communication networks, cyber attacks, such as resource depleting attacks, can cause failure of nodes and can damage or significantly slow down the convergence of the average consensus algorithm. In particular, if the network topology information is learned, an intelligent adversary can attack the most critical node in the sense that deactivating it causes the largest destruction, among all the network nodes, to the convergence speed of the average consensus algorithm. Although a centralized method can undoubtedly identify such a critical node, it requires global information and is computationally intensive and, hence, is not scalable. In this paper, we aim to identify the most critical node in a distributed manner. The network algebraic connectivity is used to assess the destruction caused by node removal and further the importance of a node. We propose three low-complexity algorithms to estimate the descent of the algebraic connectivity due to node removal and theoretically analyze the corresponding estimation errors. Based on these estimation algorithms, distributed power iteration, and maximum-consensus, we propose a fully distributed algorithm for the nodes to iteratively find the most critical one. Extensive simulation results demonstrate the effectiveness of the proposed methods.Index Terms-Consensus, critical node identification, algebraic connectivity, Fiedler vector, distributed algorithm. 1053-587X

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“…Finally, we assume that the matrix A is doubly-stochastic: its has row-sums and column-sums equal to 1. These assumptions, which are standard in the literature [31], [32], are made here for convenience, although they can be relaxed in many situations [33] without significantly changing the results. Under the assumptions mentioned above, it is well-known that A can be viewed as the probability transition matrix of an ergodic Markov chain, and the stationary distribution is uniform over the state-space S. It follows that for all sensors j ∈ S, the value z j ( ) asymptotically converges to the average of the initial values across the network:…”

Section: Gossip Communication Overhead and Error Boundsmentioning

confidence: 99%

Error Propagation in Gossip-Based Distributed Particle Filters

Gupta

Coates

Rabbat

2015

IEEE Trans. on Signal and Inf. Process. over Networks

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This paper examines the impact of the gossip procedure on distributed particle filters that employ averaging to estimate the global likelihood function. We consider a model where a gossip-driven algorithm leads to the use of a slightly distorted version of the likelihood function, in lieu of its true value. Under standard regularity conditions, and a mild assumption on the true likelihood function, we derive a time-uniform bound on the weaksense Lp error of the filter. Furthermore, we present an associated exponential inequality for the large deviations of the filter. These bounds capture the combined effects of sampling and consensusbased approximation. The results allow us to evaluate the impact of such approximations on the overall performance of the distributed particle filter, and analyze its stability. Finally, through numerical experiments, we demonstrate the practical implications of these results and explore the relationship of the performance of the filter with these theoretical error bounds.

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Convergence Speed in Distributed Consensus and Averaging

Cited by 196 publications

References 41 publications

Synchronization of Heterogeneous Oscillators Under Network Modifications: Perturbation and Optimization of the Synchrony Alignment Function

Synchronization of Heterogeneous Oscillators Under Network Modifications: Perturbation and Optimization of the Synchrony Alignment Function

Distributed Identification of the Most Critical Node for Average Consensus

Error Propagation in Gossip-Based Distributed Particle Filters

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