Distributed Optimisation With Communication Delays

TL;DR

This paper introduces a robust distributed optimization method that maintains convergence to the optimum despite communication delays in directed networks, addressing synchronization and fixed topology limitations of existing algorithms.

Contribution

A new cooperative control strategy that ensures convergence in distributed optimization over directed graphs with communication delays, overcoming synchronization and topology constraints.

Findings

Achieves convergence despite communication delays

Works over directed graphs with fixed topology

Robust to asynchronous communication

Abstract

This paper discusses distributed optimization over a directed graph. We begin with some well known algorithms which achieve consensus among agents including FROST [1], which possesses the quickest convergence to the optimum. It is a well known fact FROST has a linear convergence. However FROST works only over fixed topology of underlying network. Moreover the updates proposed therein require perfectly synchronized communication among nodes. Hence communication delays among nodes, which are inevitable in a realistic scenario, preclude the possibility of implementing FROST in real time. In this paper we introduce a co-operative control strategy which makes convergence to optimum robust to communication delays.