A Partition-Based Implementation of the Relaxed ADMM for Distributed Convex Optimization over Lossy Networks

In this paper we propose a distributed implementation of the relaxed Alternating Direction Method of Multipliers algorithm (R-ADMM) for optimization of a separable convex cost function, whose terms are stored by a set of interacting agents, one for each agent. Specifically the local cost stored by each node is in general a function of both the state of the node and the states of its neighbors, a framework that we refer to as `partition-based' optimization. This framework presents a great flexibility and can be adapted to a large number of different applications. We show that the partition-based R-ADMM algorithm we introduce is linked to the relaxed Peaceman-Rachford Splitting (R-PRS) operator which, historically, has been introduced in the literature to find the zeros of sum of functions. Interestingly, making use of non expansive operator theory, the proposed algorithm is shown to be provably robust against random packet losses that might occur in the communication between neighboring nodes. Finally, the effectiveness of the proposed algorithm is confirmed by a set of compelling numerical simulations run over random geometric graphs subject to i.i.d. random packet losses.Comment: Full version of the paper to be presented at Conference on Decision and Control (CDC) 201

An Empirical Bayes Approach for Distributed Estimation of Spatial Fields

In this paper we consider a network of spatially distributed sensors which collect measurement samples of a spatial field, and aim at estimating in a distributed way (without any central coordinator) the entire field by suitably fusing all network data. We propose a general probabilistic model that can handle both partial knowledge of the physics generating the spatial field as well as a purely data-driven inference. Specifically, we adopt an Empirical Bayes approach in which the spatial field is modeled as a Gaussian Process, whose mean function is described by means of parametrized equations. We characterize the Empirical Bayes estimator when nodes are heterogeneous, i.e., perform a different number of measurements. Moreover, by exploiting the sparsity of both the covariance and the (parametrized) mean function of the Gaussian Process, we are able to design a distributed spatial field estimator. We corroborate the theoretical results with two numerical simulations: a stationary temperature field estimation in which the field is described by a partial differential (heat) equation, and a data driven inference in which the mean is parametrized by a cubic spline

Distributed Algorithms for State Estimation in a Low Voltage Distribution Network

Sintesi di due algoritmi distribuiti e scalabili per la stima dello stato di una rete elettrica a bassa tensione (smartgrid), utilizzando oso misure di tensione e corrente ai nodi della rete. In particolare la prima tecnica si basa su una versione approssimata dell'algoritmo di Jacobi. La seconda su una formulazione scalabile della procedura ADMM (alternate direction multiplier metodo)ope

Asynchronous Distributed Optimization over Lossy Networks via Relaxed ADMM: Stability and Linear Convergence

In this work we focus on the problem of minimizing the sum of convex cost functions in a distributed fashion over a peer-to-peer network. In particular, we are interested in the case in which communications between nodes are prone to failures and the agents are not synchronized among themselves. We address the problem proposing a modified version of the relaxed ADMM, which corresponds to the Peaceman-Rachford splitting method applied to the dual. By exploiting results from operator theory, we are able to prove the almost sure convergence of the proposed algorithm under general assumptions on the distribution of communication loss and node activation events. By further assuming the cost functions to be strongly convex, we prove the linear convergence of the algorithm in mean to a neighborhood of the optimal solution, and provide an upper bound to the convergence rate. Finally, we present numerical results testing the proposed method in different scenarios.Comment: To appear in IEEE Transactions on Automatic Contro

Multi-agents adaptive estimation and coverage control using Gaussian regression

We consider a scenario where the aim of a group of agents is to perform the optimal coverage of a region according to a sensory function. In particular, centroidal Voronoi partitions have to be computed. The difficulty of the task is that the sensory function is unknown and has to be reconstructed on line from noisy measurements. Hence, estimation and coverage needs to be performed at the same time. We cast the problem in a Bayesian regression framework, where the sensory function is seen as a Gaussian random field. Then, we design a set of control inputs which try to well balance coverage and estimation, also discussing convergence properties of the algorithm. Numerical experiments show the effectivness of the new approach

Remoção de compostos sulfurados e nitrogenados do gasóleo pesado (GOP) em sistema bifásico pelo Rhodococcus erythropolis ATCC4277 em reator batelada

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Química, Florianópolis, 2014.A queima de combustíveis fósseis tem liberado uma grande quantidade de poluentes na atmosfera. A chuva ácida é extremamente prejudicial para a fauna e flora; acelera os processos de corrosão de prédios e monumentos; e gera graves problemas de saúde para o ser humano. Outro fato preocupante é a redução da qualidade do petróleo, os poços de petróleo leve estão se esgotando. Considerando esses fatores muitos países estão reformulando sua legislação a fim de exigir a comercialização de combustíveis com menores teores de impurezas. Os processos de dessulfurização e desnitrogenação existentes não são capazes de remover o enxofre e nitrogênio a níveis tão baixos. Com esse contexto tem-se desenvolvido um novo processo denominado biorremediação, o qual surge o interesse em desenvolver um processo no qual ocorre à degradação dos compostos através da ação de micro-organismos que atuam como catalisadores. A bactéria Rhodococcus erythropolis vem despontando como uma das mais promissoras na remoção e degradação de compostos indesejados do petróleo. Um estudo sobre o meio de crescimento e condições de cultivo torna-se necessário no sentido de se obter um meio nutritivo eficiente e ao mesmo tempo economicamente viável aos processos industriais. Nesse trabalho buscou-se analisar a capacidade da cepa nacional Rhodococcus erythropolis ATCC4277 de remover enxofre e nitrogênio de gasóleo pesado (GOP) em reator descontínuo utilizando concentrações de fase orgânica, com frações variando de 10 a 100% (m/m). As melhores condições de cultivo para o crescimento do R. erythropolis ATCC4277 foram temperatura de 23,7 °C, agitação de 180 rpm e com uma concentração de extrato de levedura de 6,15 g.L-1, CaCO3 de 1,1 g.L-1, glicose 2,0 g.L-1 e malte 5,0 g.L-1. O R. erythropolis ATCC4277 foi capaz de degradar os compostos de enxofre e nitrogênio presentes no gasóleo pesado, com uma remoção de 26,70 e 51,74%, respectivamente, para a fração óleo/água de 90%, resultado superior ao obtido na fração de 10%, a qual remoção foi de 7,64 e 39,02%.Abstract : The burning of fossil fuels has released a large amount of pollutants in the atmosphere. Acid rain is extremely harmful for fauna and flora; accelerates the corrosion processes of buildings and monuments; and creates serious health problems for humans. Another concerning fact is the reduction on the quality of the oil, the light oil well are being depleted. Considering these factors many countries are reformulating their laws in order to require the commercialization of fuels with lower levels of impurities. The processes of desulfurization and denitrification existing aren t capable of removing the sulfur and the nitrogen at such low levels. In this context a new process has been developed, called bioremediation, which appears into interest to develop a process in which occurs the degradation of compounds through the action of micro-organisms that act as catalysts. The bacteria Rhodococcus erythropolis has been emerging as one of the most promising agents in the removal and degradation of unwanted components of oil. A study about the growth medium becomes necessary in order to obtain not only a nutritive and efficient medium but also economically viable for the industrial processes. This work is looking for to analyze the capacity of the national strain Rhodococcus erythropolis ATCC4277 of removing sulfur and nitrogen of heavy crude oil (HCO) in a batch reactor using concentrations of the organic phase, with fractions varying from 10 to 100% (m/m). The best cultivation conditions for the growth of R. erythropolis ATCC4277 were temperature of 23,7°C, agitation of 180 rpm and with concentrations of 6,15 g.L-1 yeast extract, 1,1 g.L-1 CaCO3, 2,0 g.L-1 glucose and 5,0 g.L-1 malt. The R. erythropolis ATCC4277 was capable of degrading the components of sulfur and nitrogen present in the heavy crude oil, with a removal of 26,70 and 51,74%, respectively, for the fraction oil/water of 90%, higher result than the obtained with 10% fraction, which removal was of 7,64 and 39,02%

Smart Grid State Estimation with PMUs Time Synchronization Errors

We consider the problem of PMU-based state estimation combining information coming from ubiquitous power demand time series and only a limited number of PMUs. Conversely to recent literature in which synchrophasor devices are often assumed perfectly synchronized with the Coordinated Universal Time (UTC), we explicitly consider the presence of time-synchronization errors in the measurements due to different non-ideal causes such as imperfect satellite localization and internal clock inaccuracy. We propose a recursive Kalman-based algorithm which allows for the explicit offline computation of the expected performance and for the real-time compensation of possible frequency mismatches among different PMUs. Based on the IEEE C37.118.1 standard on PMUs, we test the proposed solution and compare it with alternative approaches on both synthetic data from the IEEE 123 node standard distribution feeder and real-field data from a small medium voltage distribution feeder located inside the EPFL campus in Lausanne.Comment: 10 page, 7 figure