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In this paper, under-directed topology, distributed coordinated tracking control schemes are proposed for multiple Euler-Lagrange systems with time-varying communication delays, nonlinear uncertainties, and external disturbances. Concerning with different leader velocities, both constant leader velocity case and time-varying leader velocity case are addressed by designing two different distributed observers. Combining with the proposed distributed leader velocity observers, two coordinated tracking control schemes are developed by the effort of neural network approximation and sliding mode technique, which can compensate the nonlinearities and uncertainties. For the first case, tracking errors are rigorously proved to be globally asymptotically converged by using Lyapunov-Krasovskii method. To further eliminate chattering caused by the discontinuous sign function, the saturation function is used for the second case, and the proposed control algorithm ensures the same convergence of tracking errors via Lyapunov analysis. Finally, the effectiveness of the proposed distributed tracking control schemes is verified by the numerical examples. INDEX TERMS Multi-agent systems, Euler-Lagrange systems, distributed tracking control, time-varying communication delay, neural network.

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