Adaptive Leader-Following Consensus for Multiple Euler-Lagrange Systems with an Uncertain Leader System

TL;DR

This paper develops an adaptive control strategy enabling multiple Euler-Lagrange systems to achieve leader-following consensus despite uncertain leader dynamics, by estimating the leader's state and system parameters through a distributed observer.

Contribution

It introduces an adaptive distributed observer and control law that handle unknown leader system matrices for Euler-Lagrange systems, advancing consensus control methods.

Findings

Successfully estimates leader's state without knowing system matrix

Achieves asymptotic learning of leader's system parameters

Ensures consensus among followers despite uncertainties

Abstract

In this paper, we study the leader-following consensus problem of multiple Euler-Lagrange systems subject to an uncertain leader system. We first establish an adaptive distributed observer for a neutrally stable linear leader system whose system matrix is not known exactly. Under standard assumptions, this adaptive distributed observer can estimate and pass the leader's state to each follower through the communication network of the system without knowing the leader's system matrix exactly. Under the additional assumption that the leader's state is persistently exciting, this adaptive distributed observer can also asymptotically learn the parameters of the leader's system matrix. On the basis of this adaptive distributed observer, we further synthesize an adaptive distributed control law to solve our problem via the certainty equivalence principle. Our result allows the leader-following consensus problem of multiple Euler-Lagrange systems to be solved even if none of the followers knows the system matrix of the leader system exactly.