Hierarchical fixed-time leader-following consensus of multiple Euler-Lagrange systems under a directed graph

This article delves into the inquiry of attaining fixed-time consensus among multiple Euler-Lagrange systems (MELSs) operating within a directed communication graph. To address this issue particularly focusing on fixed-time control with a dynamic leader, a hierarchical fixed-time control algorithm is proposed. The hierarchical algorithm comprises a distributed estimation layer and a local control layer. The introduction of this algorithm holds significant implications in advanced control strategies, furnishing an efficacious remedy to attain consensus within a fixed time span. Moreover, the theoretical proof of achieving consensus within a fixed time for MELSs under hierarchical control is established. Through the utilization of Lyapunov stability theory, we have meticulously substantiated the correctness of this algorithm. Finally, the effectiveness of the theoretical results was validated through simulation experiments.