Robust Adaptive Neural Network-Based Backstepping Tracking for Second-Order Euler-Lagrange Systems with Unknown Parameters

This paper proposes a robust adaptive tracking control scheme for a class of second-order Euler–Lagrange systems with completely unknown parameters and nonlinear dynamics. System uncertainties, including unmodeled dynamics, parametric variations, and external disturbances, are formulated as a time-varying lumped perturbation. Radial Basis Function Neural Networks (RBFNNs) approximate the unknown state-dependent nonlinear component within the perturbation bound, while adaptive laws estimate the unknown bounding constants of input-dependent terms and disturbances. By integrating backstepping with a $\sigma$-modification mechanism, a continuous adaptive control law is developed that eliminates chattering typically caused by discontinuous robust terms. Lyapunov analysis proves that all closed-loop signals are uniformly ultimately bounded, achieving asymptotic trajectory tracking with smooth control inputs. Simulations on an underactuated Unmanned Surface Vehicle (USV) under complete model uncertainty and environmental disturbances validate the effectiveness and superiority of the proposed method.