Adaptive neural network tracking control for multiple uncertain Euler–Lagrange systems with communication delays

This paper considers the distributed coordinated tracking control problems for multiple Euler–Lagrange systems with nonlinear uncertainties, external disturbances, and communication delays under the directed graph. First, distributed observers are designed such that all the followers can obtain the state information of the dynamic leader. Then, based on neural network and backstepping techniques, three distributed adaptive coordinated control algorithms are proposed to ensure that the tracking errors for each follower can be bounded. Compared with the first algorithm, the second algorithm guarantees the higher leader-following control accuracy. The third algorithm solves the chattering problem caused by discontinuous functions in the second algorithm. The closed-loop systems are investigated using the graph theory, Lyapunov theory, and Barbalat lemma. Finally, numerical examples and comparisons are provided to show the effectiveness and the performance of the proposed methods.