Hierarchical Prescribed-Time Time-Varying Formation Tracking for Multiple Euler-Lagrange Systems with Input-to-Output Redundancy and Matrix-Weighted Diagraph

This article focuses on the resolution of the challenge related to the time-varying formation tracking (TVFT) for multiple Euler-Lagrange systems (MELSs), achieving prescribed-time convergence under matrix-weighted diagraph in task-space, where all the uncertain dynamic terms, external disturbances as well as input-to-state redundancy are taken into account. To tackle these aforementioned issues, an innovative hierarchical prescribed-time control (HPTC) strategy is introduced, structured into two main components. Additionally, a two-layer hierarchical control framework is proposed. Subsequently, several sufficient conditions corresponding to solving such TVFT problem are established by virtue of Lyapunov stability analysis. Eventually, the numerical simulations provided a rigorous validation of the theoretical findings, confirming their feasibility and efficacy.