Leaderless Consensus of Heterogeneous Multiple Euler-Lagrange Systems with Unknown Disturbance

TL;DR

This paper addresses the challenge of achieving leaderless consensus among heterogeneous Euler-Lagrange systems under persistent unknown disturbances, by developing a distributed control approach that combines observers, internal model, and adaptive regulation.

Contribution

It introduces a novel distributed control scheme for Euler-Lagrange systems that enables consensus and disturbance rejection without a common reference model or trajectory.

Findings

Successfully achieves group model learning for Euler-Lagrange systems over directed networks.

Handles persistent unknown disturbances with unknown biases, amplitudes, phases, and frequencies.

Extends recent linear agent results to nonlinear Euler-Lagrange dynamics.

Abstract

This paper studies the leaderless consensus problem of {heterogeneous} multiple networked Euler-Lagrange systems subject to persistent disturbances with unknown constant biases, amplitudes, initial phases, and frequencies. The main characteristic of this study is that none of the agents has information of a common reference model or of a common reference trajectory. Therefore, the agents must simultaneously and in a distributed way: achieve consensus to a common reference model (group model); achieve consensus to a common reference trajectory; {and} reject the unknown disturbances. We show that this is possible via a suitable combination of techniques of distributed `observers', internal model principle, and adaptive regulation. The proposed design generalizes recent results on group model learning, which have been studied for linear agents over undirected networks. In this work, group model learning is achieved for Euler-Lagrange dynamics over directed networks in the presence of persistent unknown disturbances.