The fundamental goal presented in this manuscript is designing a robust controller using the basis of the integral variant of the sliding mode theory of the averaged sub-gradient that may regulate the robotic manipulator movement. In addition, the proposed controller includes analysis to handle the actuators’ dynamics that force the manipulator’s movement. For the manipulator class in this study, each motor (direct current) operates as an actuator driven by a power converter circuit. The controller is devised sequentially, yielding a backstepping-like formulation that considers the actuator dynamics under internal uncertainties and external perturbations. The suggested control strategy solves the trajectory tracking formulation for the end-effector positioning, implementing a set of averaged sub-gradient integral sliding mode controllers. The controller also uses a complementary adaptive approximation corresponding to the uncertain section of the robotic arm dynamics. The proposed approximation is based on a differential neural network with learning laws developed using a variant of a controlled Lyapunov function. The key result of this study confirms that the minimisation of a function is obtained depending on the tracking position error of the end effector. Furthermore, a set of numerical evaluations illustrates the efficiency of the robust controller based on the aggregation of the averaged formulation and the continuous dynamics neural network. Indeed, the proposed control strategy forces a smaller value for the functional compared with the one evaluated under the effect of a state-feedback control.