Backstepping-based distributed coordinated tracking for multiple uncertain Euler-Lagrange systems

Based on the idea of backstepping design, distributed coordinated tracking problems under directed topology are discussed for multiple Euler-Lagrange (EL) systems. The dynamic leader case is considered. First, with the parameter-linearity property, a distributed coordinated adaptive control scheme is proposed for EL systems in the presence of parametric uncertainties. Then, subject to nonlinear uncertainties and external disturbances, an improved adaptive control algorithm is developed by using neural-network (NN) approximation of nonlinear functions. Both proposed algorithms can make tracking errors for each follower ultimately bounded. The closed-loop systems are investigated by using the combination of graph theory, Lyapunov theory, and Barbalat Lemma. Numerical examples and comparisons with other methods are provided to show the effectiveness of the proposed control strategies.