Adaptive neural dynamic surface control of mechanical systems using integral terminal sliding mode

•We present a new dynamic surface control (DSC) method for fully-actuated mechanical systems.•We incorporate integral terminal sliding mode (TSM) terms into the conventional DSC error surfaces.•We use raised-cosine radial basis functions (RBFs) to adaptively estimate the uncertainty/disturbances upper-bound.•We show the closed-loop stability as well as the tracking error convergence by Lyapunov-based analysis. This paper studies the robust tracking control problem of fully-actuated mechanical systems using a novel integral dynamics surface control (DSC) method. We replace the conventional DSC error surfaces with new nonlinear integral surfaces to generate a quasi-terminal sliding mode (TSM) in the tracking error trajectories. Then, we follow the recursive, Lyapunov-based design procedure of the DSC to obtain the control law. The resultant quasi-TSM adjusts the error convergence rate according to the distance from the origin. To achieve robustness against structural variations of the mechanical system as well as external disturbances, we use nonlinear damping combined with a radial basis function neural network (RBFNN) approximator. The RBFNN adaptively identifies the upper-bound of the uncertainty/disturbances to prevent conservative, high-gain control inputs. Moreover, we use raised-cosine basis functions, which have compact supports, to improve the computational efficiency of the RBFNN. Through Lyapunov-based stability analysis, we show the boundedness and ultimate boundedness of the closed-loop system as well as the TSM-induced convergence of the tracking errors. Detailed numerical simulations support the efficacy of the proposed control method.