The purpose of this study is to present the design of robust control based on the integral sliding mode control version of the averaged subgradient for a robotic manipulator considering the dynamics of the direct current motor, which is driven by a power converter electrical device. The control action is sequentially developed in the subsystems of the complete model, realizing the so-called backstepping (or cascade) approach, including the perturbed dynamics of the actuator. The proposed control strategy for solving the trajectory tracking problem in each stage implements the averaged subgradient-version of the integral sliding mode technique. The controller design solution is treated as optimizing a suitable convex (not obligatory strongly convex) cost functional, depending on the tracking error and reaching its minimal value at the origin of the error tracking space. The main result of this study shows that the minimization of the proposed functional leads to the optimal tracking regime in the presence of significant uncertainties in the mathematical model of the power converter. A numerical example proves the effectiveness of the suggested robust dynamic controller. The comparison between the obtained trajectory tracking results and the outcomes produced by standard proportional integral derivative (PID) controllers is presented. The proposed controller exhibits a better tracking of the reference trajectory than the PID version, showing a smaller mean square estimation for the tracking error.