Barrier Lyapunov function-based robust adaptive neural network control with dynamically adjusted activation functions for Euler–Lagrange systems under position constraints

This paper proposes a novel robust control strategy with position constraints for a class of Euler–Lagrange systems. The approach integrates an adaptive neural network estimator to compensate for parametric uncertainties while ensuring accurate trajectory tracking. A key feature of the proposed method is the iterative online adjustment of the activation function centers in the neural networks, which significantly enhances its ability to capture time-varying nonlinearities—beyond what conventional fixed-center neural network structures can achieve. The primary objective is to guarantee precise trajectory tracking, while the secondary objective is to ensure that the tracking error remains strictly within a predefined region, thereby regulating transient behavior and limiting overshoot. To achieve this, a barrier Lyapunov function is incorporated into the control design, enforcing state constraints and ensuring that all closed-loop signals remain bounded. Rigorous Lyapunov-based stability analysis is provided, and numerical simulations on a two degree of freedom robotic manipulator demonstrate the effectiveness and robustness of the proposed control framework under system uncertainties and external disturbances.