Fixed-time Synchronization of Networked Uncertain Euler-Lagrange Systems

TL;DR

This paper develops a fixed-time control method for multi-agent Euler-Lagrange systems with uncertainties, ensuring synchronization within a predetermined time regardless of initial states.

Contribution

It introduces a novel distributed fixed-time observer and a backstepping-based controller for uncertain Euler-Lagrange systems under directed networks.

Findings

Achieves synchronization in fixed time independent of initial conditions.

Provides relaxed conditions for finite-time convergence.

Ensures robust performance with parametric uncertainties.

Abstract

This paper considers the fixed-time control problem of a multi-agent system composed of a class of Euler-Lagrange dynamics with parametric uncertainty and a dynamic leader under a directed communication network. A distributed fixed-time observer is first proposed to estimate the desired trajectory and then a fixed-time controller is constructed by transforming uncertain Euler-Lagrange systems into second-order systems and utilizing the backstepping design procedure. The overall design guarantees that the synchronization errors converge to zero in a prescribed time independent of initial conditions. The control design conditions can also be relaxed for a weaker finite-time control requirement.