This study aims to present the design of robust control based on the integral sliding mode control version of the averaged sub-gradient for a robotic manipulator considering the dynamics of the direct current motor device driven by a power converter electrical system. The control action is sequentially operated, developing a class of back-stepping approaches, including the perturbed dynamics of the actuator. The proposed control strategy for solving the end-effector trajectory tracking problem in each stage implements the averaged subgradient-version of the integral sliding mode technique aided with an adaptive approximation of the robotic arm dynamics using an artificial neural network with differential evolution. The main result of this study shows that the minimization of the proposed functional leads to the optimal tracking regime. A numerical example proves the effectiveness of the suggested robust dynamic controller. The proposed controller exhibits a better tracking of the reference trajectory than the state feedback version.