Adaptive neural-network coordinated tracking control of multiple Euler-Lagrange systems with communication delays

Considering communication delays, the coordinated tracking control problems of multiple Euler-Lagrange systems under a directed graph are investigated. The information of the static leader is available to only a subset of the followers. First, the distributed observer is designed so that the state information of the leader can be estimated by every follower. Then, considering model nonlinear uncertainties and external disturbances, two distributed adaptive control algorithms based on neural networks are proposed to make sure that the tracking errors for every follower can be bounded and asymptotically convergent, respectively. The closed-loop systems are investigated by using the Lyapunov theory and the graph theory. Numerical simulations are provided to verify the effectiveness of the proposed methods.