Predefined-time-synchronized bipartite formation control for networked heterogeneous Euler–Lagrange systems

This paper intends to address the predefined-time-synchronized (PTS) bipartite time-varying formation (BTVF) tracking control issue of networked heterogeneous Euler–Lagrange systems (NHELSs) with unknown disturbance. In contrast to prior formation control schemes, the considered PTS strategy aims to drive all state components of the NHELS task-space converge into the equilibrium at the same time, with the synchronized settling time being predefined in advance. An improved hierarchical control strategy, including a distributed estimator layer and a local control layer, is presented to achieve this performance. The distributed estimator layer is tasked with estimating the desired state vectors. The local control layer first involves a novel predefined-time algebraic reconstruction approach to reconstruct the unknown disturbance. Then, given the combination of the switching sliding-mode technique and norm-normalized sign function, a singularity-free control law is proposed to achieve the PTS BTVF control. Finally, simulations and comparisons on two and three degrees-of-freedom manipulators are carried out to testify the feasibility and superiority of the theoretical results.