Flocking of networked uncertain Euler–Lagrange systems on directed graphs

This paper investigates the flocking problem of networked nonlinear Euler–Lagrange systems with parametric uncertainties, and they are assumed to interact on directed graphs with a directed spanning tree. We propose an adaptive controller to achieve the flocking objective, and the resultant closed-loop networked system bears the cascade structure. Using a new similarity decomposition approach, a critical-characteristic-root based approach, and the input–output stability analysis, we demonstrate the convergence of the position/velocity synchronization errors among the uncertain nonlinear Euler–Lagrange agents. We also show that the velocities of the Euler–Lagrange systems converge to the weighted average velocity value. Simulation results are provided to demonstrate the performance of the proposed controller.