Robust Prescribed Time Control of Euler-Lagrange Systems

This article aims to develop a robust prescribed time controller for precise trajectory tracking for uncertain Euler-Lagrange systems with unknown time-varying disturbances without prior knowledge of their upper bounds. The control strategy involves utilizing a scaled transformation function to map the standard error system to a scaled error system. The presented controller is developed based on the scaled error system, incorporating state-dependent control gains and yielding a model-free controller structure. Distinguishing from previous methods, the designed controller takes a different approach by avoiding the direct multiplication of feedback terms with the estimated inertia matrix. The developed strategy mitigates the adverse effects of mismatches between the actual and estimated inertia matrices. A novel Lyapunov-based stability analysis is employed to establish fixed-time input-to-state stability within the prescribed time and to ensure the convergence of error signals to the origin. Experimental validation on a three-degree-of-freedom planar robot arm confirms the effectiveness of the proposed controller.