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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 133 (3 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.
Distributed Function Calculation and Consensus Using Linear Iterative Strategies
, 2007
"... Given an arbitrary network of interconnected nodes, we develop and analyze a distributed strategy that enables a subset of the nodes to calculate any given function of the node values. Our scheme utilizes a linear iteration where, at each timestep, each node updates its value to be a weighted avera ..."
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Cited by 47 (12 self)
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Given an arbitrary network of interconnected nodes, we develop and analyze a distributed strategy that enables a subset of the nodes to calculate any given function of the node values. Our scheme utilizes a linear iteration where, at each timestep, each node updates its value to be a weighted average of its own previous value and those of its neighbors. We show that this approach can be viewed as a linear dynamical system, with dynamics that are given by the weight matrix of the linear iteration, and with outputs for each node that are captured by the set of values that are available to that node at each timestep. In networks with timeinvariant topologies, we use observability theory to show that after running the linear iteration for a finite number of timesteps with almost any choice of weight matrix, each node obtains enough information to calculate any arbitrary function of the initial node values. The problem of distributed consensus via linear iterations, where all nodes in the network calculate the same function, is treated as a special case of our approach. In particular, our scheme allows nodes in networks with timeinvariant topologies to reach consensus on any arbitrary function of the initial node values in a finite number of steps for almost any choice of weight matrix.
Distributed control of robotic networks: a mathematical approach to motion coordination algorithms
, 2009
"... (i) You are allowed to freely download, share, print, or photocopy this document. (ii) You are not allowed to modify, sell, or claim authorship of any part of this document. (iii) We thank you for any feedback information, including errors, suggestions, evaluations, and teaching or research uses. 2 ..."
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Cited by 41 (1 self)
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(i) You are allowed to freely download, share, print, or photocopy this document. (ii) You are not allowed to modify, sell, or claim authorship of any part of this document. (iii) We thank you for any feedback information, including errors, suggestions, evaluations, and teaching or research uses. 2 “Distributed Control of Robotic Networks ” by F. Bullo, J. Cortés and S. Martínez
An overview of recent progress in the study of distributed multiagent coordination
, 2012
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Finitetime consensus problems for networks of dynamic agents
 IEEE Transactions on Automatic Control
, 2010
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A gossip algorithm for convex consensus optimization over networks,” submitted for publication in
 IEEE Transactions on Automatic Control,
, 2010
"... AbstractIn many applications, nodes in a network wish to achieve not only a consensus, but an optimal one. To date, a family of subgradient algorithms have been proposed to solve this problem under general convexity assumptions. This paper shows that, with a few additional mild assumptions, a fund ..."
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Cited by 14 (1 self)
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AbstractIn many applications, nodes in a network wish to achieve not only a consensus, but an optimal one. To date, a family of subgradient algorithms have been proposed to solve this problem under general convexity assumptions. This paper shows that, with a few additional mild assumptions, a fundamentally different, nongradientbased algorithm with appealing features can be constructed. Specifically, we develop Pairwise Equalizing (PE), a gossipstyle, distributed asynchronous iterative algorithm for achieving unconstrained, separable, convex consensus optimization over undirected networks with timevarying topologies, where each component function is strictly convex, continuously differentiable, and has a minimizer. We show that PE is easy to implement, bypasses limitations facing the subgradient algorithms, and produces a switched, nonlinear, networked dynamical system that is deterministically and stochastically asymptotically convergent. Moreover, we show that PE admits a common Lyapunov function and reduces to the wellstudied Pairwise Averaging and Randomized Gossip Algorithm in a special case.
Decentralized finitetime sliding mode estimators and their applications in decentralized finitetime formation tracking
 Systems & Control Letters
, 2010
"... AbstractIn this paper, a simple but efficient framework is proposed to achieve finitetime decentralized formation tracking of multiple autonomous vehicles with the introduction of decentralized sliding mode estimators. First, we propose and study both firstorder and secondorder decentralized sl ..."
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Cited by 12 (2 self)
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AbstractIn this paper, a simple but efficient framework is proposed to achieve finitetime decentralized formation tracking of multiple autonomous vehicles with the introduction of decentralized sliding mode estimators. First, we propose and study both firstorder and secondorder decentralized sliding mode estimators. In particular, we show that the proposed firstorder decentralized sliding mode estimator can guarantee accurate position estimation in finite time and the proposed secondorder decentralized sliding mode estimator can guarantee accurate position and velocity estimation in finite time. Then the decentralized sliding mode estimators are employed to achieve decentralized formation tracking of multiple autonomous vehicles. In particular, it is shown that formation tracking can be achieved for systems with both singleintegrator kinematics and doubleintegrator dynamics in finite time. Because accurate estimation can be achieved in finite time by using the decentralized sliding mode estimators, many formation tracking/flying scenarios can be easily decoupled into two subtasks, that is, decentralized sliding mode estimation and vehicle desired state tracking, without imposing a stringent condition on the information flow.
Distributed decision through selfsynchronizing sensor networks in the presence of propagation delays and asymmetric channels
 IEEE Transactions on Signal Processing
, 2008
"... In this paper we propose and analyze a distributed algorithm for achieving globally optimal decisions, either estimation or detection, through a selfsynchronization mechanism among linearly coupled integrators initialized with local measurements. We model the interaction among the nodes as a direct ..."
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Cited by 11 (5 self)
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In this paper we propose and analyze a distributed algorithm for achieving globally optimal decisions, either estimation or detection, through a selfsynchronization mechanism among linearly coupled integrators initialized with local measurements. We model the interaction among the nodes as a directed graph with weights (possibly) dependent on the radio channels and we pose special attention to the effect of the propagation delay occurring in the exchange of data among sensors, as a function of the network geometry. We derive necessary and sufficient conditions for the proposed system to reach a consensus on globally optimal decision statistics. One of the major results proved in this work is that a consensus is reached with exponential convergence speed for any bounded delay condition if and only if the directed graph is quasistrongly connected. We provide a closed form expression for the global consensus, showing that the effect of delays is, in general, the introduction of a bias in the final decision. Finally, we exploit our closed form expression to devise a doublestep consensus mechanism able to provide an unbiased estimate with minimum extra complexity, without the need to know or estimate the channel parameters. 1
Selftriggered coordination with ternary controllers
"... Abstract: This paper regards coordination of networked systems with ternary controllers. We develop a hybrid coordination system which implements a selftriggered communication policy, based on polling the neighbors upon need. We prove that the proposed scheme ensures finitetime convergence to a ne ..."
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Cited by 9 (5 self)
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Abstract: This paper regards coordination of networked systems with ternary controllers. We develop a hybrid coordination system which implements a selftriggered communication policy, based on polling the neighbors upon need. We prove that the proposed scheme ensures finitetime convergence to a neighborhood of the consensus state. We estimate both the size of the error neighborhood, and the time and communication costs, as functions of the sensitivity of the quantizer: our analysis highlights natural tradeoffs between accuracy of consensus and costs. In the same hybrid selftriggered framework, we also design a timevarying controller which asymptotically drives the system to consensus.