Distributed function calculation and consensus using linear iterative strategies

Shreyas Sundaram

doi:10.1109/JSAC.2008.080507

Return

Distributed function calculation and consensus using linear iterative strategies

2008-05-01

119

PRE

Shreyas Sundaram *

Christoforos N. Hadjicostis

DOI：10.1109/JSAC.2008.080507

Original

Original request for help

Save

Abstract

En 中文

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 time-step. 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 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 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.

Keywords:

distributed function calculation

distributed consensus

observability theory

structural observability

networked control

multi-agent systems

AI Summary

Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.