Distributed Coordination of Multiple Unknown Euler-Lagrange Systems

Abstract

A robust consensus tracking problem is addressed for multiple unknown Euler-Lagrange systems where only a subset of the agents is informed of the desired time-varying trajectory. Challenging unstructured uncertainties, including unknown nonlinear dynamics and disturbances, are considered in the agent dynamics. A model-free, identifier-based, continuous, distributed robust control method is designed to solve this problem under both undirected and directed graphs. The control inputs and coupling gains depend only on local information and the consensus tracking errors are proven to converge to zero asymptotically. Under an undirected graph, a distributed nonlinear identifier is developed for each agent to compensate for the unknown nonlinear dynamics and disturbances. Based on this identifier, a continuous distributed control law is designed to enable asymptotic robust consensus tracking. By selecting the gains of the designed controller according to the derived conditions, closed-loop stability is proven using graph theory and Lyapunov analysis. Furthermore, the directed graph case is investigated via a distributed two-layer coordination scheme in which a model-free continuous distributed controller is designed by using information obtained from a distributed leader estimator. Numerical simulation results are given to illustrate the effectiveness of the proposed methods.