Distributed bipartite time-varying formation tracking control with prescribed-time convergence for heterogeneous Euler-Lagrange systems

This paper focuses on the study of the prescribed-time bipartite time-varying formation tracking (BTVFT) problem for multiple heterogeneous Euler-Lagrange systems (HELSs) with external disturbances under directed signed graphs. Considering the fact that the states of leader cannot be accurately obtained, a set of observers which can estimate the states of the leader within a prescribed time, is firstly established according to the time-varying function. Subsequently, a prescribed-time distributed control protocol is proposed by employing a terminal sliding surface, aiming to achieve the BTVFT under digraphs within a prescribed time. The theoretical proof utilizes suitable Lyapunov functions to demonstrate that the control law can guide the state trajectories of each follower to the corresponding terminal sliding surface within a predefined time, thus ensuring the solution to the BTVFT problem of HELSs. Finally, simulation results are provided to validate the effectiveness of the derived findings.