Using a linear gain to accelerate average consensus over unreliable networks

International audience— Packet loss is a serious issue in wireless consensus networks, as even few failures might prevent a network to converge to the correct value. However, it is possible to compensate for the errors caused by packet collisions, by modifying the updating weights. Such a modification compensates for the loss of information in an unreliable network, but results in a reduced convergence speed. In this paper, we propose a faster method – based on a suitable gain in the consensus dynamics – to solve the unreliable average consensus problem. We find a sufficient condition for the gain to preserve stability of the network. Simulations are used to discuss the choice of the gain, and to compare our method with the literature

A geometrically converging dual method for distributed optimization over time-varying graphs

In this paper we consider a distributed convex optimization problem over time-varying undirected networks. We propose a dual method, primarily averaged network dual ascent (PANDA), that is proven to converge R-linearly to the optimal point given that the agents objective functions are strongly convex and have Lipschitz continuous gradients. Like dual decomposition, PANDA requires half the amount of variable exchanges per iterate of methods based on DIGing, and can provide with practical improved performance as empirically demonstrated.Comment: Submitted to Transactions on Automatic Contro

Distributed estimation from relative measurements of heterogeneous and uncertain quality

This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes connected by an edge. In order to model heterogeneity and uncertainty of the measurements, we assume them to be affected by additive noise distributed according to a Gaussian mixture. In this original setup, we formulate the problem of computing the Maximum-Likelihood (ML) estimates and we design two novel algorithms, based on Least Squares regression and Expectation-Maximization (EM). The first algorithm (LS- EM) is centralized and performs the estimation from relative measurements, the soft classification of the measurements, and the estimation of the noise parameters. The second algorithm (Distributed LS-EM) is distributed and performs estimation and soft classification of the measurements, but requires the knowledge of the noise parameters. We provide rigorous proofs of convergence of both algorithms and we present numerical experiments to evaluate and compare their performance with classical solutions. The experiments show the robustness of the proposed methods against different kinds of noise and, for the Distributed LS-EM, against errors in the knowledge of noise parameters.Comment: Submitted to IEEE transaction

Achieving robust average consensus over lossy wireless networks

International audienceAverage consensus over unreliable wireless networks can be impaired by losses. In this paper we study a novel method to compensate for the lost information, when packet collisions cause transmitter-based random failures. This compensation makes the network converge to the average of the initial states of the network, by modifying the weights of the links to accommodate for the topology changes due to packet losses. Additionally, a gain is used to increase the convergence speed, and an analysis of the stability of the network is performed, leading to a criterion to choose such gain to guarantee network stability. For the implementation of the compensation method, we propose a new distributed algorithm, which uses both synchronous and asynchronous mechanisms to achieve consensus and to deal with uncertainty in packet delivery. The theoretical results are then confirmed by simulations