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75
Consensus and cooperation in networked multiagent systems
 Proceedings of the IEEE
"... Summary. This paper provides a theoretical framework for analysis of consensus algorithms for multiagent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, timedelays, and performance guarantees. An over ..."
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Cited by 279 (2 self)
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Summary. This paper provides a theoretical framework for analysis of consensus algorithms for multiagent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, timedelays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in smallworld networks, Markov processes and gossipbased algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with latticetype nearest neighbor interactions. Simulation results are presented that demonstrate the role of smallworld effects on the speed of consensus algorithms and cooperative control of multivehicle formations.
A scheme for robust distributed sensor fusion based on average consensus
 Proceedings of the International Conference on Information Processing in Sensor Networks (IPSN
, 2005
"... Abstract — We consider a network of distributed sensors, where each sensor takes a linear measurement of some unknown parameters, corrupted by independent Gaussian noises. We propose a simple distributed iterative scheme, based on distributed average consensus in the network, to compute the maximum ..."
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Cited by 140 (3 self)
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Abstract — We consider a network of distributed sensors, where each sensor takes a linear measurement of some unknown parameters, corrupted by independent Gaussian noises. We propose a simple distributed iterative scheme, based on distributed average consensus in the network, to compute the maximumlikelihood estimate of the parameters. This scheme doesn’t involve explicit pointtopoint message passing or routing; instead, it diffuses information across the network by updating each node’s data with a weighted average of its neighbors ’ data (they maintain the same data structure). At each step, every node can compute a local weighted leastsquares estimate, which converges to the global maximumlikelihood solution. This scheme is robust to unreliable communication links. We show that it works in a network with dynamically changing topology, provided that the infinitely occurring communication graphs are jointly connected. I.
Geographic Gossip: Efficient Aggregation for Sensor Networks
 in Proc. Information Processing in Sensor Networks (IPSN
, 2006
"... Gossip algorithms for aggregation have recently received significant attention for sensor network applications because of their simplicity and robustness in noisy and uncertain environments. However, gossip algorithms can waste significant energy by essentially passing around redundant information m ..."
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Cited by 80 (4 self)
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Gossip algorithms for aggregation have recently received significant attention for sensor network applications because of their simplicity and robustness in noisy and uncertain environments. However, gossip algorithms can waste significant energy by essentially passing around redundant information multiple times. For realistic sensor network model topologies like grids and random geometric graphs, the inefficiency of gossip schemes is caused by slow mixing times of random walks on those graphs. We propose and analyze an alternative gossiping scheme that exploits geographic information. By utilizing a simple resampling method, we can demonstrate substantial gains over previously proposed gossip protocols. In particular, for random geometric graphs, our algorithm computes the true average to accuracy 1/n a using O(n 1.5 √ log n) radio transmissions, which reduces the energy consumption by a algorithms. q n factor over standard gossip log n
Belief consensus and distributed hypothesis testing in sensor networks
 Network Embedded Sensing and Control. (Proceedings of NESC’05 Worskhop), volume 331 of Lecture Notes in Control and Information Sciences
, 2006
"... Summary. In this paper, we address distributed hypothesis testing (DHT) in sensor networks and Bayesian networks using the averageconsensus algorithm of OlfatiSaber & Murray. As a byproduct, we obtain a novel belief propagation algorithm called Belief Consensus. This algorithm works for connected ..."
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Cited by 35 (1 self)
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Summary. In this paper, we address distributed hypothesis testing (DHT) in sensor networks and Bayesian networks using the averageconsensus algorithm of OlfatiSaber & Murray. As a byproduct, we obtain a novel belief propagation algorithm called Belief Consensus. This algorithm works for connected networks with loops and arbitrary degree sequence. Belief consensus allows distributed computation of products of n beliefs (or conditional probabilities) that belong to n different nodes of a network. This capability enables distributed hypothesis testing for a broad variety of applications. We show that this belief propagation admits a Lyapunov function that quantifies the collective disbelief in the network. Belief consensus benefits from scalability, robustness to link failures, convergence under variable topology, asynchronous features of averageconsensus algorithm. Some connections between smallword networks and speed of convergence of belief consensus are discussed. A detailed example is provided for distributed detection of multitarget formations in a sensor network. The entire network is capable of reaching a common set of beliefs associated with correctness of different hypotheses. We demonstrate that our DHT algorithm successfully identifies a test formation in a network of sensors with selfconstructed statistical models. Key words: distributed hypothesis testing, multitarget tracking, Bayesian networks, average consensus, belief propagation, sensor networks, smallworld networks 1
Information Fusion for Wireless Sensor Networks: Methods, Models, and Classifications
"... Wireless sensor networks produce a large amount of data that needs to be processed, delivered, and assessed according to the application objectives. The way these data are manipulated by the sensor nodes is a fundamental issue. Information fusion arises as a response to process data gathered by sens ..."
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Cited by 33 (2 self)
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Wireless sensor networks produce a large amount of data that needs to be processed, delivered, and assessed according to the application objectives. The way these data are manipulated by the sensor nodes is a fundamental issue. Information fusion arises as a response to process data gathered by sensor nodes and benefits from their processing capability. By exploiting the synergy among the available data, information fusion techniques can reduce the amount of data traffic, filter noisy measurements, and make predictions and inferences about a monitored entity. In this work, we survey the current stateoftheart of information fusion by presenting the known methods, algorithms, architectures, and models of information fusion, and
Consensus in Ad Hoc WSNs With Noisy Links—Part II: Distributed Estimation and Smoothing of Random Signals
"... Abstract—Distributed algorithms are developed for optimal estimation of stationary random signals and smoothing of (even nonstationary) dynamical processes based on generally correlated observations collected by ad hoc wireless sensor networks (WSNs). Maximum a posteriori (MAP) and linear minimum me ..."
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Cited by 31 (5 self)
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Abstract—Distributed algorithms are developed for optimal estimation of stationary random signals and smoothing of (even nonstationary) dynamical processes based on generally correlated observations collected by ad hoc wireless sensor networks (WSNs). Maximum a posteriori (MAP) and linear minimum meansquare error (LMMSE) schemes, well appreciated for centralized estimation, are shown possible to reformulate for distributed operation through the iterative (alternatingdirection) method of multipliers. Sensors communicate with singlehop neighbors their individual estimates as well as multipliers measuring how far local estimates are from consensus. When iterations reach consensus, the resultant distributed (D) MAP and LMMSE estimators converge to their centralized counterparts when intersensor communication links are ideal. The DMAP estimators do not require the desired estimator to be expressible in closed form, the DLMMSE ones are provably robust to communication or quantization noise and both are particularly simple to implement when the data model is linearGaussian. For decentralized tracking applications, distributed Kalman filtering and smoothing algorithms are derived for anytime MMSE optimal consensusbased state estimation using WSNs. Analysis and corroborating numerical examples demonstrate the merits of the novel distributed estimators. Index Terms—Distributed estimation, Kalman smoother, nonlinear optimization, wireless sensor networks (WSNs).
Geographic gossip: Efficient averaging for sensor networks
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2008
"... Gossip algorithms for distributed computation are attractive due to their simplicity, distributed nature, and robustness in noisy and uncertain environments. However, using standard gossip algorithms can lead to a significant waste of energy by repeatedly recirculating redundant information. For re ..."
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Cited by 28 (5 self)
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Gossip algorithms for distributed computation are attractive due to their simplicity, distributed nature, and robustness in noisy and uncertain environments. However, using standard gossip algorithms can lead to a significant waste of energy by repeatedly recirculating redundant information. For realistic sensor network model topologies like grids and random geometric graphs, the inefficiency of gossip schemes is related to the slow mixing times of random walks on the communication graph. We propose and analyze an alternative gossiping scheme that exploits geographic information. By utilizing geographic routing combined with a simple resampling method, we demonstrate substantial gains over previously proposed gossip protocols. For regular graphs such as the ring or grid, our algorithm improves standard gossip by factors of and, respectively. For the more challenging case of random geometric graphs, our algorithm computes the true average to accuracy using 1 5 1 ( ( log) log) radio transmissions, which yields a log factor improvement over standard gossip algorithms. We illustrate these theoretical results with experimental comparisons between our algorithm and standard methods as applied to various classes of random fields.
Distributed Kalman filtering based on consensus strategies
, 2007
"... In this paper, we consider the problem of estimating the state of a dynamical system from distributed noisy measurements. Each agent constructs a local estimate based on its own measurements and estimates from its neighbors. Estimation is performed via a two stage strategy, the first being a Kalman ..."
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Cited by 21 (0 self)
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In this paper, we consider the problem of estimating the state of a dynamical system from distributed noisy measurements. Each agent constructs a local estimate based on its own measurements and estimates from its neighbors. Estimation is performed via a two stage strategy, the first being a Kalmanlike measurement update which does not require communication, and the second being an estimate fusion using a consensus matrix. In particular we study the interaction between the consensus matrix, the number of messages exchanged per sampling time, and the Kalman gain. We prove that optimizing the consensus matrix for fastest convergence and using the centralized optimal gain is not necessarily the optimal strategy if the number of exchanged messages per sampling time is small. Moreover, we showed that although the joint optimization of the consensus matrix and the Kalman gain is in general a nonconvex problem, it is possible to compute them under some important scenarios. We also provide some numerical examples to clarify some of the analytical results and compare them with alternative estimation strategies.
Gossip along the way: Orderoptimal consensus through randomized path averaging
 IN PROC. 45TH ANNU. ALLERTON CONF. COMMUNICATION, CONTROL, COMPUTING
, 2007
"... Gossip algorithms have recently received significant attention, mainly because they constitute simple and robust algorithms for distributed information processing over networks. However for many topologies that are realistic for wireless adhoc and sensor networks (like grids and random geometric ..."
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Cited by 17 (1 self)
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Gossip algorithms have recently received significant attention, mainly because they constitute simple and robust algorithms for distributed information processing over networks. However for many topologies that are realistic for wireless adhoc and sensor networks (like grids and random geometric graphs), the standard nearestneighbor gossip converges very slowly. A recently proposed algorithm called geographic gossip improves gossip efficiency by a p n / log n factor for random geometric graphs, by exploiting geographic information of node locations. In this paper we prove that a variation of geographic gossip that averages along routed paths, improves efficiency by an additional p n / log n factor and is order optimal for grids and random geometric graphs. Our analysis provides some general techniques and can be used to provide bounds on the performance of randomized message passing algorithms operating over various graph topologies.
Incremental stochastic subgradient algorithms for convex optimization
 SIAM J. Optim
"... Abstract. In this paper we study the effect of stochastic errors on two constrained incremental subgradient algorithms. We view the incremental subgradient algorithms as decentralized network optimization algorithms as applied to minimize a sum of functions, when each component function is known o ..."
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Cited by 15 (6 self)
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Abstract. In this paper we study the effect of stochastic errors on two constrained incremental subgradient algorithms. We view the incremental subgradient algorithms as decentralized network optimization algorithms as applied to minimize a sum of functions, when each component function is known only to a particular agent of a distributed network. We first study the standard cyclic incremental subgradient algorithm in which the agents form a ring structure and pass the iterate in a cycle. We consider the method with stochastic errors in the subgradient evaluations and provide sufficient conditions on the moments of the stochastic errors that guarantee almost sure convergence when a diminishing stepsize is used. We also obtain almost sure bounds on the algorithm’s performance when a constant stepsize is used. We then consider the Markov randomized incremental subgradient method, which is a noncyclic version of the incremental algorithm where the sequence of computing agents is modeled as a time nonhomogeneous Markov chain. Such a model is appropriate for mobile networks, as the network topology changes across time in these networks. We establish the convergence results and error bounds for the Markov randomized method in the presence of stochastic errors for diminishing and constant stepsizes, respectively. 1. Introduction. A