Backstepping-Based Distributed Finite-Time Coordinated Tracking Control for Multiple Uncertain Euler–Lagrange Systems

Based on the backstepping control theory, this paper investigates the distributed finite-time coordinated tracking control for Euler–Lagrange systems under directed graphs. We consider that only a portion of followers can receive information from the dynamic leader. Two cases are discussed in this paper: (1) the system having parameter uncertainties which can be linearized, and (2) the system having structured uncertainties and external disturbances which cannot be linearized. For the first case, parameter-linearity property is used to approximate the parametric uncertainties. For the second case, neural networks are used to approximate the nonlinear uncertainties and external disturbances. For the controller design, first, we design an auxiliary variable. Then, backstepping method and Lyapunov stability theory are used to prove that the tracking errors and adaptive estimation errors are bounded. Finally, the finite-time convergence property of the tracking errors is proved by increasing control gains. Numerical examples and comparisons with other methods are provided to show the effectiveness and superiorities of the proposed methods.