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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 ..."
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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.
Stochastic approximation for consensus seeking: mean square and almost sure convergence
 in Proceedings of the 46th IEEE Conference on Decision and Control
"... Abstract — We consider stochastic consensus problems in strongly connected directed graph models where each agent has noisy measurements of its neighbors ’ states. For consensus seeking, we develop stochastic approximation type algorithms with a decreasing step size and establish mean square and alm ..."
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Cited by 25 (1 self)
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Abstract — We consider stochastic consensus problems in strongly connected directed graph models where each agent has noisy measurements of its neighbors ’ states. For consensus seeking, we develop stochastic approximation type algorithms with a decreasing step size and establish mean square and almost sure convergence of the agents ’ states to the same limit. I.
Consensus in Networked MultiAgent Systems with Adversaries
"... In the past decade, numerous consensus protocols for networked multiagent systems have been proposed. Although some forms of robustness of these algorithms have been studied, reaching consensus securely in networked multiagent systems, in spite of intrusions caused by malicious agents, or adversar ..."
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Cited by 11 (6 self)
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In the past decade, numerous consensus protocols for networked multiagent systems have been proposed. Although some forms of robustness of these algorithms have been studied, reaching consensus securely in networked multiagent systems, in spite of intrusions caused by malicious agents, or adversaries, has been largely underexplored. In this work, we consider a general model for adversaries in Euclidean space and introduce a consensus problem for networked multiagent systems similar to the Byzantine consensus problem in distributed computing. We present the Adversarially Robust Consensus Protocol (ARCP), which combines ideas from consensus algorithms that are resilient to Byzantine faults and from linear consensus protocols used for control and coordination of dynamic agents. We show that ARCP solves the consensus problem in complete networks whenever there are more cooperative agents than adversaries. Finally, we illustrate the resilience of ARCP to adversaries through simulations and compare ARCP with a linear consensus protocol for networked multiagent systems.
Stochastic double array analysis and convergence of consensus algorithms with noisy measurements
 Proc. American Control Conference
, 2007
"... Abstract — This paper considers consensusseeking of networked agents in an uncertain environment where each agent has noisy measurements of its neighbors ’ states. We propose stochastic approximation type algorithms with a decreasing step size. We first establish consensus results in a twoagent mo ..."
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Cited by 8 (3 self)
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Abstract — This paper considers consensusseeking of networked agents in an uncertain environment where each agent has noisy measurements of its neighbors ’ states. We propose stochastic approximation type algorithms with a decreasing step size. We first establish consensus results in a twoagent model via a stochastic double array analysis. Next, we generalize the analysis to a class of well studied symmetric models and obtain consensus results. I.
Powerdelay analysis of consensus algorithms on wireless networks with interference
 Int. J. Syst., Control Commun
"... We study the convergence of the average consensus algorithm in wireless networks in the presence of interference. For regular lattices with periodic boundary conditions, we characterize the convergence properties of an optimal MAC protocol that maximizes the speed of convergence on these networks. ..."
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Cited by 6 (2 self)
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We study the convergence of the average consensus algorithm in wireless networks in the presence of interference. For regular lattices with periodic boundary conditions, we characterize the convergence properties of an optimal MAC protocol that maximizes the speed of convergence on these networks. We extend this analysis to hierarchical networks with a backbone of communication nodes supporting randomly placed sensor nodes. We provide analytical upper and lower bounds for the convergence rate for these networks. Our results show that in an interferencelimited scenario the fastest converging interconnection topology for the consensus algorithm crucially depends on the geometry of node placement. In particular, we prove that asymptotically in the number of nodes, increasing the transmit power to allow long range interconnections improves the convergence rate in onedimensional tori, while it has the opposite effect in higher dimensions. Index TermsConsensus algorithms, interference, MAC protocol, wireless networks.
Effect of Network Geometry and Interference on Consensus in Wireless Networks
"... Abstract We study the convergence of the average consensus algorithm in wireless networks in the presence of interference. It is wellknown that convergence of the consensus algorithm improves with network connectivity. However, from a networking standpoint, highly connected wireless networks may ha ..."
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Abstract We study the convergence of the average consensus algorithm in wireless networks in the presence of interference. It is wellknown that convergence of the consensus algorithm improves with network connectivity. However, from a networking standpoint, highly connected wireless networks may have lower throughput because of increased interference. This raises an interesting question: What is the effect of increased network connectivity on the convergence of the consensus algorithm, given that this connectivity comes at the cost of lower network throughput? We address this issue for two types of networks: regular lattices with periodic boundary conditions, and a hierarchical network where a backbone of nodes arranged as a regular lattice supports a collection of randomly placed nodes. We characterize the properties of an optimal TDMA protocol that maximizes the speed of convergence on these networks and provide analytical upper and lower bounds for the achievable convergence rate. Our results show that in a interferencelimited scenario the fastest converging interconnection topology for the consensus algorithm crucially depends on the geometry of node placement. In particular, we prove that asymptotically in the number of nodes, forming longrange interconnections improves the convergence rate in onedimensional tori, while it has the opposite effect in higher dimensions.
IV. NUMERICAL EXAMPLE Consider the case when and
"... Fig. 2 shows the disturbance signals. Finally, the reference signal is shown in Fig. 3 (upper plot). The linear matrix inequality of Theorem 2 is feasible in this case and The lower plot in Fig. 3 confirms that the overall design task is achieved and the next stage would be to attempt to tune the de ..."
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Fig. 2 shows the disturbance signals. Finally, the reference signal is shown in Fig. 3 (upper plot). The linear matrix inequality of Theorem 2 is feasible in this case and The lower plot in Fig. 3 confirms that the overall design task is achieved and the next stage would be to attempt to tune the design. V. CONCLUSIONS The major contributions in this short paper are i) the application of lifting techniques to transform the bidirectional dynamics into those of an equivalent unidirectional repetitive process model and hence the availability of a stability theory and control law design to achieve this basic property, and ii) the first results on stability plus performance in the case when there are disturbances present, which are assumed to be periodic over twice the pass length. Also there is clearly much work to do before these results can be evaluated on physical examples. This includes a wide range of algorithms for control law design, robustness
IV. NUMERICAL EXAMPLE Consider the case when and
"... Fig. 2 shows the disturbance signals. Finally, the reference signal is shown in Fig. 3 (upper plot). The linear matrix inequality of Theorem 2 is feasible in this case and The lower plot in Fig. 3 confirms that the overall design task is achieved and the next stage would be to attempt to tune the de ..."
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Fig. 2 shows the disturbance signals. Finally, the reference signal is shown in Fig. 3 (upper plot). The linear matrix inequality of Theorem 2 is feasible in this case and The lower plot in Fig. 3 confirms that the overall design task is achieved and the next stage would be to attempt to tune the design. V. CONCLUSIONS The major contributions in this short paper are i) the application of lifting techniques to transform the bidirectional dynamics into those of an equivalent unidirectional repetitive process model and hence the availability of a stability theory and control law design to achieve this basic property, and ii) the first results on stability plus performance in the case when there are disturbances present, which are assumed to be periodic over twice the pass length. Also there is clearly much work to do before these results can be evaluated on physical examples. This includes a wide range of algorithms for control law design, robustness
Convergence Rate for Stochastic Consensus Algorithms with TimeVarying Noise Statistics: Asymptotic Normality
"... Abstract — This paper studies consensus seeking over noisy networks with timevarying noise statistics. Stochastic approximation type algorithms can ensure consensus in mean square and with probability one. For performance evaluation, we examine the long term behavior of the approximation error whi ..."
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Abstract — This paper studies consensus seeking over noisy networks with timevarying noise statistics. Stochastic approximation type algorithms can ensure consensus in mean square and with probability one. For performance evaluation, we examine the long term behavior of the approximation error which consists of two naturally defined components. We show that the two components and their sum are each asymptotically normal after being normalized by the square root of time. This, in turn, characterizes the convergence rate of the algorithm. We also give the asymptotic formula for the scaled error covariances. I.