Adaptive Fixed-time Bipartite Consensus Tracking for Multiple Euler-Lagrange Systems Under Asymmetric Input Constraint

This work is concerned with the fixed-time bipartite consensus tracking (BCT) problem for multiple Euler-Lagrange systems (MELSs) with asymmetric input constraint. Firstly, a fixed-time distributed observer (FTDO) is constructed to capture the leader's states. Then, the adaptive local control protocol (LCP) is designed to ensure that the followers' trajectories converge to the leader's trajectory within fixed time. Besides, a hyperbolic tangent function is used to deal with the issue of asymmetric saturation. With the Lyapunov stability theory, it is proved that all errors are semi-global fixed-time stable. Eventually, a numerical example is presented to show the validity of the proposed method.