Distributed function calculation and consensus using linear iterative strategies
Date
2008Source
IEEE Journal on Selected Areas in CommunicationsVolume
26Issue
4Pages
650-660Google Scholar check
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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 time-step, 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 connected networks with time-invariant topologies, we use observability theory to show that after running the linear iteration for a finite number of time-steps with almost anychoice 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 connected networks with time-invariant 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. © 2006 IEEE.