A Randomized Gossip Consenus Algorithm on Convex Metric Spaces

Abstract

A consensus problem consists of a group of dynamic agents who seek to agree upon certain quantities of interest. This problem can be generalized in the context of convex metric spaces that extend the standard notion of convexity. In this paper we introduce and analyze a randomized gossip algorithm for solving the generalized consensus problem on convex metric spaces. We study the convergence properties of the algorithm using stochastic differential equations theory. We show that the dynamics of the distances between the states of the agents can be upper bounded by the dynamics of a stochastic differential equation driven by Poisson counters. In addition, we introduce instances of the generalized consensus algorithm for several examples of convex metric spaces together with numerical simulations.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2012
Accession Number
ADA588967

Entities

People

  • Christoforos Somarakis
  • Ion Matei
  • John Baras

Organizations

  • University of Maryland

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Consensus Algorithms
  • Convergence
  • Differential Equations
  • Dynamics
  • Eigenvalues
  • Equations
  • Mathematics
  • Network Topology
  • Networks
  • Probability
  • Random Variables
  • Real Numbers
  • Simulations
  • Standards
  • Topology

Fields of Study

  • Mathematics

Readers

  • Agent-Based Social Robotics and Mobile-Assisted Learning in Virtual Environments.
  • Mathematical Modeling and Probability Theory.
  • Operations Research

Technology Areas

  • Space