## 1 Introduction
### Scope and Contributions of This Paper  
The ML and deep RL techniques considered in this paper have great potential for mechanical engineering applications that are not well explored in the literature. Basically, there are two key points. First, RL methods allow for developing effective nonlinear controllers of mechanical systems that, to some extent, ignore the underlying physical behavior of the dynamical system to be controlled. In fact, the mechanical system to be controlled is treated as a black-box external environment from which input and output data are collected. This allows for using the same strategy for the control design in a large variety of state-space systems. As discussed in the paper, the control designer is called to develop an appropriate shape of the reward function that is more suitable for the engineering problem to be considered. Second, by using the post-training approach devised in this paper, one can design a robust control policy. Therefore, its performance is still satisfactory when some environment parameters are changed because of model uncertainty or due to other unpredictable phenomena. To investigate these two key points, a benchmark problem of nonlinear control is employed in the paper, namely the swing-up maneuver of the cart-pole system. The presence of dry friction is also considered to assess the robustness of the proposed approach. The difficulties related to traditional robust control systems with uncertainties in their physical parameters are often discussed in the literature. On the other hand, controllers based on reinforcement learning employ neural networks to represent the actuation policy. Thus, these present robust performance by virtue of the generalization capability of neural networks. Such robustness is exploited and improved in this work by employing a post-training of an optimal control policy in modified environments. The study of the swing-up problem for the cart-pole system is one of the most common examples found in the literature as a benchmark problem to exemplify utilizing numerical experiments to test the effectiveness of a novel approach for designing a nonlinear controller. Thus, the scope and the contributions of this work are to study the robustness of an RL-based control system, specifically developed and applied to the swing-up task of the cart-pole system, and to address the issue of data efficiency in real-world implementations. This is performed through a parametric study of a trained policy represented by a multilayer perceptron. The main procedure consists of evaluating the behavior of the control system under modified environments that feature modifications of the cart-pole physical properties. This, to the best of the authors' knowledge, was only briefly investigated in an RL controller with a simplified friction force approximated as damping in [57]. In contrast, the dry friction model employed in the present work is more accurate. Therefore, this paper is the first work in which the proposed control method based on deep reinforcement learning techniques is thoroughly developed and tested considering the dry friction phenomena. Additionally, modifications are considered for the mass of the cart, the mass and length of the pendulum, as well as the dry friction coefficient. These are varied in reasonable ranges to test the robustness of the control law devised in this paper. Besides, a method is proposed to further extend the agent capability in a data-efficient way by performing a subsequent training of the agent neural networks in a modified environment in the presence of dry friction. To this end, dry friction is modeled as a smoothed function of the instant normal force between the road and the environment. The findings of this work are based on extensive numerical experiments and result in a promising methodology for improvements in data efficiency and robustness for real systems' implementation.