Distributed Fixed-time Formation-containment Control for Multiple Euler-Lagrange Systems with Directed Graphs

Abstract

In this paper, the distributed fixed-time formation-containment (DFTFC) problem of multiple Euler-Lagrange systems with parametric uncertainties and input disturbances is studied under directed graphs. First, a distributed fixed-time sliding-mode estimator is constructed to estimate the desired states of each robot with that only parts of followers can access the information of leaders. Next, based on the estimator, a distributed fixed-time formation control algorithm is developed to drive leaders to achieve a specified formation. Then, the distributed fixed-time containment control algorithm is proposed for followers with its estimated states being tracked in a fixed time. Note that an explicit upper bound of the convergence time of DFTFC control algorithm is obtained independent of initial conditions. Finally, numerical simulations are performed to show the effectiveness of the obtained theoretical results.