Actor–Critic Predefined-Time Adaptive Tracking Control for Partially Unknown Euler–Lagrange Systems

This paper studies predefined-time trajectory tracking for Euler–Lagrange systems with composite uncertainties encompassing partially known dynamics, parametric variations, and bounded disturbances. A two-step backstepping architecture is developed. In Step 1, a predefined-time virtual control law is constructed for the position subsystem. In Step 2, an energy-based torque controller is designed for the velocity subsystem using nominal model compensation, adaptive parameter estimation, actor neural network approximation of residual dynamics, a critic network for performance-oriented learning, and a continuous robust term. A rigorous Lyapunov analysis shows that all closed-loop signals are uniformly ultimately bounded and that the tracking errors converge to a computable residual set within a predefined time for all initial conditions contained in the selected compact set. Comparative simulations on a 2-DOF planar manipulator demonstrate that the proposed method provides faster convergence and improved steady-state tracking accuracy than both a PID baseline and a classical Slotine–Li adaptive baseline, while respecting the predefined-time bound.