Random Asynchronous Iterations in Distributed Coordination Algorithms

TL;DR

This paper investigates the convergence of distributed coordination algorithms under random asynchronous updates, showing they reach consensus under broad stochastic conditions without requiring independence or Markov properties.

Contribution

It demonstrates that even non-SIA stochastic matrices can ensure consensus through random asynchronous iterations under general stochastic conditions.

Findings

Consensus achieved with non-SIA matrices

Convergence holds under broad stochastic assumptions

Asynchronous iterations are effective without independence or Markov constraints

Abstract

Distributed coordination algorithms (DCA) carry out information processing processes among a group of networked agents without centralized information fusion. Though it is well known that DCA characterized by an SIA (stochastic, indecomposable, aperiodic) matrix generate consensus asymptotically via synchronous iterations, the dynamics of DCA with asynchronous iterations have not been studied extensively, especially when viewed as stochastic processes. This paper aims to show that for any given irreducible stochastic matrix, even non-SIA, the corresponding DCA lead to consensus successfully via random asynchronous iterations under a wide range of conditions on the transition probability. Particularly, the transition probability is neither required to be independent and identically distributed, nor characterized by a Markov chain.