Robust Finite-Time Dynamic Average Consensus With Exponential Convergence Rates

This brief focuses on the dynamic weighted average consensus problem and aims to achieve accurate tracking of the weighted average of all the time-varying reference signals in a network. We first propose a robust dynamic weighted average consensus (RDWAC) algorithm that employs a simple fixed control gain and introduces an individual weight for each agent compared with recent works. Furthermore, a theoretical finite-time convergence analysis instead of an asymptotic one is provided by constructing a novel Lyapunov function, which shows that the accurate weighted average consensus can be reached exponentially within a finite time interval. In addition, the lower bound of the required convergence time is given and the relationship between the lower bound and the initial steady-state error and control parameters is established explicitly. Finally, some numerical examples are given to illustrate the effectiveness of the proposed algorithm.

I. Introduction

Given a connected network with a group of agents each of which has its own local time-varying reference signal, dynamic average consensus (DAC) aims to design a distributed algorithm to ensure that each agent can track the average of all the time-varying reference signals by exchanging local information with its neighbors [1]. During the past decade, there has been more and more attention devoted to dynamic average consensus due to its significance in various applications such as formation control [2], sensor fusion [3], robotic manipulator control [4], [5] and distributed optimization [6], [7].