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

Abstract 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.