Distributed finite-time containment control for multiple Euler-Lagrange systems with communication delays

In this paper, distributed finite-time containment control for multiple Euler-Lagrange systems with communication delays and general disturbances is investigated under directed topology by using sliding-mode control technique. We consider that the information of dynamic leaders can be obtained by only a portion of the followers. Firstly, a nonsingular fast terminal sliding surface is selected to achieve the finite-time convergence for the error variables. Then, a distributed finite-time containment control algorithm is proposed where the neural network is utilized to approximate the model uncertainties and external disturbances of the systems. Furthermore, considering that error constraint method can improve the performance of the systems, a distributed finite-time containment control algorithm is developed by transforming the error variable into another form. It is demonstrated that the containment errors are bounded in finite time by using Lyapunov theory, graph theory, and finite-time stability theory. Numerical simulations are provided to show the effectiveness of the proposed methods.