Finite-Time and Fixed-Time Bipartite Consensus of Multiple Euler–Lagrange Systems via Hierarchical Control Algorithm

This paper investigates the finite-time and fixed-time bipartite consensus problem of multiple Euler–Lagrange systems (MELSs) under directed interaction topologies, considering external disturbances. Two novel distributed hierarchical control algorithms are developed to address the challenging problems. Specifically, a new distributed estimator is designed to estimate the states of agents in finite/fixed-time. Moreover, based on the obtained estimations, the finite/fixed-time controller is presented to accomplish the bipartite consensus of the MELSs in the local control layer. By utilizing Lyapunov stability and the nearest neighbor-interactions theory, sufficient conditions for achieving the designed performance of the MELSs are derived. Simulation examples are provided to illustrate the effectiveness of the proposed algorithms.