Finite-time physics-informed adaptive super-twisting control for energy-efficient actuator-saturated robotic manipulators

Conventional sliding-mode and neural adaptive controllers rarely ensure explicit finite-time stability under actuator saturation and often overlook energy-efficient control allocation. This work introduces a physics-informed adaptive super-twisting sliding-mode controller (PI-Adaptive STSMC) for a three-link planar manipulator. Actuator limits are modeled as input-saturation nonlinearities and analytically addressed as bounded matched disturbances within the Lyapunov framework. A lightweight neural adaptation module continuously updates the super-twisting gains based on real-time tracking errors. A Lyapunov-consistent Softplus-and-clipping projection ensures all gain updates remain within finite-time stable bounds. The network is pre-trained in a differentiable physics-based simulator using a loss function that incorporates Lagrangian dynamics, torque limits, control effort, and saturation avoidance. To our knowledge, this is the first controller to combine physics-informed neural adaptation with super-twisting SMC under explicit actuator saturation while maintaining formal finite-time convergence guarantees. Simulations demonstrate identical tracking accuracy to fixed-gain STSMC, with 60–65% lower energy use under ±5 Nm limits and 15–20% lower consumption under ±2 Nm, without chattering or convergence delays. Comparative and ablation analyses confirm that both neural adaptation and stability-certified projection are essential; removing either mechanism reduces robustness, safety, or efficiency. These results show that physics-informed gain adaptation enables finite-time stable, saturation-aware, and energy-efficient robotic control. Certifying neural updates through Lyapunov-consistent projection and modeling saturation as a matched perturbation ensures smooth, stable, and resource-aware torque regulation. This approach provides a certified pathway for energy-aware and safety-critical intelligent control in advanced robotic systems.