EDCHO: High Order Exact Dynamic Consensus

TL;DR

This paper introduces EDCHO, a high order exact dynamic consensus algorithm that achieves zero steady-state error for the average of time-varying signals in multi-agent systems using high order sliding modes.

Contribution

It presents a novel distributed differentiator-based consensus algorithm that guarantees exact convergence and can also reach consensus on higher derivatives of the average signal.

Findings

Achieves zero steady-state error for time-varying signals.

Ensures stability and convergence in undirected connected graphs.

Demonstrates effectiveness through simulation scenarios.

Abstract

This article addresses the problem of average consensus in a multi-agent system when the desired consensus quantity is a time varying signal. Although this problem has been addressed in existing literature by linear schemes, only bounded steady-state errors have been achieved. Other approaches have used first order sliding modes to achieve zero steady-state error, but suffer from the chattering effect. In this work, we propose a new exact dynamic consensus algorithm which leverages high order sliding modes, in the form of a distributed differentiator to achieve zero steady-state error of the average of time varying reference signals in a group of agents. Moreover, our proposal is also able to achieve consensus to high order derivatives of the average signal, if desired. An in depth formal study on the stability and convergence for EDCHO is provided for undirected connected graphs. Finally, the effectiveness and advantages of our proposal are shown with concrete simulation scenarios.