Neural network-based predefined-time bipartite formation tracking control of uncertain heterogeneous Euler-Lagrange systems in task space.

The main problem addressed in this paper is the task-space bipartite formation tracking problem of uncertain heterogeneous Euler-Lagrange systems in predefined time. To solve this problem, an effective hierarchical predefined-time control algorithm is designed. This algorithm utilizes a non-singular sliding surface, allowing for the adjustment of the upper bound of the settling time as a flexible parameter. Key components of the proposed approach include an estimator for the leader's states and a controller tailored to the formation problem. To mitigate the effects of dynamic uncertainties in the system, the radial basis function neural network is integrated into the methodology. Finally, the effectiveness and validity of the proposed algorithm are demonstrated through numerical simulations, showcasing their practical applicability and efficacy.