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118
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.
Distributed average consensus with leastmeansquare deviation
 Journal of Parallel and Distributed Computing
, 2005
"... We consider a stochastic model for distributed average consensus, which arises in applications such as load balancing for parallel processors, distributed coordination of mobile autonomous agents, and network synchronization. In this model, each node updates its local variable with a weighted averag ..."
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Cited by 82 (5 self)
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We consider a stochastic model for distributed average consensus, which arises in applications such as load balancing for parallel processors, distributed coordination of mobile autonomous agents, and network synchronization. In this model, each node updates its local variable with a weighted average of its neighbors ’ values, and each new value is corrupted by an additive noise with zero mean. The quality of consensus can be measured by the total meansquare deviation of the individual variables from their average, which converges to a steadystate value. We consider the problem of finding the (symmetric) edge weights that result in the least meansquare deviation in steady state. We show that this problem can be cast as a convex optimization problem, so the global solution can be found efficiently. We describe some computational methods for solving this problem, and compare the weights and the meansquare deviations obtained by this method and several other weight design methods.
Consensus propagation
 IEEE Transactions on Information Theory
"... Abstract — We propose consensus propagation, an asynchronous distributed protocol for averaging numbers across a network. We establish convergence, characterize the convergence rate for regular graphs, and demonstrate that the protocol exhibits better scaling properties than pairwise averaging, an a ..."
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Cited by 61 (6 self)
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Abstract — We propose consensus propagation, an asynchronous distributed protocol for averaging numbers across a network. We establish convergence, characterize the convergence rate for regular graphs, and demonstrate that the protocol exhibits better scaling properties than pairwise averaging, an alternative that has received much recent attention. Consensus propagation can be viewed as a special case of belief propagation, and our results contribute to the belief propagation literature. In particular, beyond singlyconnected graphs, there are very few classes of relevant problems for which belief propagation is known to converge. Index Terms — belief propagation, distributed averaging, distributed consensus, distributed signal processing, Gaussian Markov random fields, messagepassing algorithms, maxproduct algorithm, minsum algorithm, sumproduct algorithm. I.
Quantized consensus
, 2007
"... We study the distributed averaging problem on arbitrary connected graphs, with the additional constraint that the value at each node is an integer. This discretized distributed averaging problem models several problems of interest, such as averaging in a network with finite capacity channels and loa ..."
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Cited by 56 (0 self)
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We study the distributed averaging problem on arbitrary connected graphs, with the additional constraint that the value at each node is an integer. This discretized distributed averaging problem models several problems of interest, such as averaging in a network with finite capacity channels and load balancing in a processor network. We describe simple randomized distributed algorithms which achieve consensus to the extent that the discrete nature of the problem permits. We give bounds on the convergence time of these algorithms for fully connected networks and linear networks.
Convergence speed in distributed consensus and averaging
 IN PROC. OF THE 45TH IEEE CDC
, 2006
"... We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove ..."
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Cited by 52 (1 self)
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We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove lower bounds on the worstcase convergence time for various classes of linear, timeinvariant, distributed consensus methods, and provide an algorithm that essentially matches those lower bounds. We then consider the case of a timevarying topology, and provide a polynomialtime averaging algorithm.
On Distributed Averaging Algorithms and Quantization Effects
, 2009
"... We consider distributed iterative algorithms for the averaging problem over timevarying topologies. Our focus is on the convergence time of such algorithms when complete (unquantized) information is available, and on the degradation of performance when only quantized information is available. We stu ..."
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Cited by 47 (13 self)
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We consider distributed iterative algorithms for the averaging problem over timevarying topologies. Our focus is on the convergence time of such algorithms when complete (unquantized) information is available, and on the degradation of performance when only quantized information is available. We study a large and natural class of averaging algorithms, which includes the vast majority of algorithms proposed to date, and provide tight polynomial bounds on their convergence time. We also describe an algorithm within this class whose convergence time is the best among currently available averaging algorithms for timevarying topologies. We then propose and analyze distributed averaging algorithms under the additional constraint that agents can only store and communicate quantized information, so that they can only converge to the average of the initial values of the agents within some error. We establish bounds on the error and tight bounds on the convergence time, as a function of the number of quantization levels.
Stabilization of planar collective motion with limited communication
 IEEE Trans. Automat. Contr
"... Abstract—This paper proposes a design methodology to stabilize relative equilibria in a model of identical, steered particles moving in the plane at unit speed. Relative equilibria either correspond to parallel motion of all particles with fixed relative spacing or to circular motion of all particle ..."
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Cited by 41 (21 self)
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Abstract—This paper proposes a design methodology to stabilize relative equilibria in a model of identical, steered particles moving in the plane at unit speed. Relative equilibria either correspond to parallel motion of all particles with fixed relative spacing or to circular motion of all particles around the same circle. Particles exchange relative information according to a communication graph that can be undirected or directed and timeinvariant or timevarying. The emphasis of this paper is to show how previous results assuming alltoall communication can be extended to a general communication framework. Index Terms—Cooperative control, geometric control, multiagent systems, stabilization. I.
Connections Between Cooperative Control and Potential Games Illustrated on the Consensus Problem
, 2007
"... This paper presents a view of cooperative control using the language of learning in games. We review the game theoretic concepts of potential games and weakly acyclic games and demonstrate how the specific cooperative control problem of consensus can be formulated in these settings. Motivated by th ..."
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Cited by 35 (15 self)
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This paper presents a view of cooperative control using the language of learning in games. We review the game theoretic concepts of potential games and weakly acyclic games and demonstrate how the specific cooperative control problem of consensus can be formulated in these settings. Motivated by this connection, we build upon game theoretic concepts to better accommodate a broader class of cooperative control problems. In particular, we introduce sometimes weakly acyclic games for timevarying objective functions and action sets, and provide distributed algorithms for convergence to an equilibrium. Finally, we illustrate how to implement these algorithms for the consensus problem in a variety of settings, most notably, in an environment with nonconvex obstructions.
Synchronization and balancing on the Ntorus
 Systems and Control Letters
"... In this paper, we study the behavior of a network of N agents, each evolving on the circle. We propose a novel algorithm that achieves synchronization or balancing in phase models under mild connectedness assumptions on the (possibly timevarying and unidirectional) communication graphs. The global ..."
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Cited by 27 (14 self)
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In this paper, we study the behavior of a network of N agents, each evolving on the circle. We propose a novel algorithm that achieves synchronization or balancing in phase models under mild connectedness assumptions on the (possibly timevarying and unidirectional) communication graphs. The global convergence analysis on the Ntorus is a distinctive feature of the present work with respect to previous results that have focused on convergence in the Euclidean space.
Monitoring environmental boundaries with a robotic sensor network
, 2006
"... Abstract — In this paper we propose and analyze an algorithm to monitor an environmental boundary with mobile sensors. The objective is to optimally approximate the boundary with a polygon. The mobile sensors rely only on sensed local information to position some interpolation points and define an a ..."
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Cited by 23 (7 self)
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Abstract — In this paper we propose and analyze an algorithm to monitor an environmental boundary with mobile sensors. The objective is to optimally approximate the boundary with a polygon. The mobile sensors rely only on sensed local information to position some interpolation points and define an approximating polygon. We design algorithms that distribute the vertices of the approximating polygon uniformly along the boundary. The notion of uniform placement relies on a metric inspired by known results on approximation of convex bodies. The algorithm is provably convergent for static boundaries and also for slowlymoving boundaries because of certain inputtostate stability properties. I.