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60
Gossip algorithms for distributed signal processing
 PROCEEDINGS OF THE IEEE
, 2010
"... Gossip algorithms are attractive for innetwork processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the co ..."
Abstract

Cited by 116 (30 self)
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Gossip algorithms are attractive for innetwork processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This paper presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmittedmessages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.
Distributing the Kalman filters for largescale systems
 IEEE Trans. on Signal Processing, http://arxiv.org/pdf/0708.0242
"... Abstract—This paper presents a distributed Kalman filter to estimate the state of a sparsely connected, largescale,dimensional, dynamical system monitored by a network of sensors. Local Kalman filters are implemented ondimensional subsystems,, obtained by spatially decomposing the largescale sys ..."
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Cited by 55 (11 self)
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Abstract—This paper presents a distributed Kalman filter to estimate the state of a sparsely connected, largescale,dimensional, dynamical system monitored by a network of sensors. Local Kalman filters are implemented ondimensional subsystems,, obtained by spatially decomposing the largescale system. The distributed Kalman filter is optimal under an th order Gauss–Markov approximation to the centralized filter. We quantify the information loss due to this thorder approximation by the divergence, which decreases as increases. The order of the approximation leads to a bound on the dimension of the subsystems, hence, providing a criterion for subsystem selection. The (approximated) centralized Riccati and Lyapunov equations are computed iteratively with only local communication and loworder computation by a distributed iterate collapse inversion (DICI) algorithm. We fuse the observations that are common among the local Kalman filters using bipartite fusion graphs and consensus averaging algorithms. The proposed algorithm achieves full distribution of the Kalman filter. Nowhere in the network, storage, communication, or computation ofdimensional vectors and matrices is required; only dimensional vectors and matrices are communicated or used in the local computations at the sensors. In other words, knowledge of the state is itself distributed. Index Terms—Distributed algorithms, distributed estimation, information filters, iterative methods, Kalman filtering, largescale systems, matrix inversion, sparse matrices. I.
Distributed Integral Action: Stability Analysis and Frequency
 Control of Power Systems,” in IEEE Annual Conference on Decision and Control (CDC
, 2012
"... Abstract—This paper analyzes distributed proportionalintegral controllers. We prove that integral action can be successfully applied to consensus algorithms, where attenuation of static disturbances is achieved. These control algorithms are applied to decentralized frequency control of electrical p ..."
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Cited by 12 (3 self)
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Abstract—This paper analyzes distributed proportionalintegral controllers. We prove that integral action can be successfully applied to consensus algorithms, where attenuation of static disturbances is achieved. These control algorithms are applied to decentralized frequency control of electrical power systems. We show that the proposed algorithm can attenuate step disturbances of power loads. We provide simulations of the proposed control algorithm on the IEEE 30 bus test system that demonstrate its efficiency. I.
Distributed state estimation for discretetime sensor networks with randomly varying nonlinearities and missing measurements
 IEEE Transactions on Neural Networks
, 2011
"... Abstract — This paper deals with the distributed state estimation problem for a class of sensor networks described by discretetime stochastic systems with randomly varying nonlinearities and missing measurements. In the sensor network, there is no centralized processor capable of collecting all the ..."
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Cited by 7 (3 self)
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Abstract — This paper deals with the distributed state estimation problem for a class of sensor networks described by discretetime stochastic systems with randomly varying nonlinearities and missing measurements. In the sensor network, there is no centralized processor capable of collecting all the measurements from the sensors, and therefore each individual sensor needs to estimate the system state based not only on its own measurement but also on its neighboring sensors ’ measurements according to certain topology. The stochastic Brownian motions affect both the dynamical plant and the sensor measurement outputs. The randomly varying nonlinearities and missing measurements are introduced to reflect more realistic dynamical behaviors of the sensor networks that are caused by noisy environment as well as by probabilistic communication failures. Through available output measurements from each individual sensor, we aim to design distributed state estimators to approximate the states of the networked dynamic system. Sufficient conditions are presented to guarantee the convergence of the estimation error systems for all admissible stochastic disturbances, randomly varying nonlinearities, and missing measurements. Then, the explicit expressions of individual estimators are derived to facilitate the distributed computing of state estimation from each sensor. Finally, a numerical example is given to verify the theoretical results. Index Terms — Distributed state estimation, missing measurements, randomly varying nonlinearity, sensor network, stochastic disturbances. I.
Efficient Information Aggregation Strategies for Distributed Control and Signal Processing
, 2010
"... ..."
Distributed Weight Balancing over Digraphs
"... A weighted digraph is balanced if, for each node, the sum of the weights of the edges outgoing from that node is equal to the sum of the weights of the edges incoming to that node. Weightbalanced digraphs play a key role in a number of applications, including cooperative control, distributed optimi ..."
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Cited by 4 (2 self)
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A weighted digraph is balanced if, for each node, the sum of the weights of the edges outgoing from that node is equal to the sum of the weights of the edges incoming to that node. Weightbalanced digraphs play a key role in a number of applications, including cooperative control, distributed optimization, and distributed averaging. We propose distributed algorithms that operate over static topologies, for solving the weight balancing problem when the weights are either nonnegative real numbers or when they are restricted to be nonnegative integers. For the case of real weights, the proposed algorithm is shown to admit geometric convergence rate. For the case of integer weights, the proposed algorithm is shown to converge after a finite number of iterations that we explicitly bound. We also provide examples to illustrate the operation, performance, and potential advantages of the proposed algorithms.
Distributed estimation through randomized gossip Kalman filter
 In Proc. 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference. Shanghai, pages 7049 7054
, 2009
"... Abstract—In this paper we consider the problem of estimating a random process from noisy measurements, collected by a sensor network. We analyze a distributed two–stage algorithm. The first stage is a Kalman–like estimate update, in which each agent makes use only of its own measurements. During th ..."
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Cited by 3 (1 self)
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Abstract—In this paper we consider the problem of estimating a random process from noisy measurements, collected by a sensor network. We analyze a distributed two–stage algorithm. The first stage is a Kalman–like estimate update, in which each agent makes use only of its own measurements. During the second phase agents communicate with their neighbors to improve their estimate. Estimate fusion is operated by running a consensus iteration. In literature it has been considered only the case of a fixed communication strategies, i.e. described by a fixed constant consensus matrix. However, in many practical cases this is just a rough model of communications in a sensor network, that usually happen according to a randomized strategy. This strategy is more properly modeled by assuming that the consensus matrices are drawn, according to a selection probability, from an alphabet of matrices compatible with the communication graph, at each time instant. This work deals therefore with randomized communication strategies and in particular with the symmetric gossip. A mean square performance analysis is carried out and an upper–bound for the trace of the estimation error variance is derived. The proposed upper–bound has to be considered the main technical contribution of the present paper, since it is based on a highly non–trivial inequality on matrix singular values, proved in the appendix. This upper–bound is a good performance assessment index and it is assumed therefore as a cost function to be minimized. We show moreover that problem of minimizing this cost function by choosing the Kalman gain and the selection probability is convex in each of the two variables separately although it is not jointly convex. Finally simulations are presented and the results discussed. I.