## 1 Introduction  
From a very early age, control has played a fundamental role in society, being currently present in most systems with several control techniques. Among the most used algorithms, the Proportional-Integral-Derivative (PID) controller stands out, which is part of the classic control methods [1, 2]. However, with scientific and technological developments in the field of Artificial Intelligence (AI), there are now control techniques called intelligent control, which include methods such as fuzzy control, evolutionary control, and neural control [3, 4, 5, 6]. Neural networks are now widely studied and used in the areas of image processing [7, 8], complex optimization problems [9], systems control [10], among others. By applying AI techniques like neural networks to a control system, the algorithms obtained are capable of solving problems that classical control cannot, due to the universal approximation capabilities of the neural networks. In control systems, the objective is to find an appropriate feedback function that maps the measured outputs in order to control the inputs. For that, there are several architectures that use neural networks that can be employed [11, 12]. This type of control can be applied to several types of systems; however, its performance stands out compared to other techniques in the control of nonlinear and unstable systems [13, 14]. Magnetic levitation consists of the suspension of an object in the air, using magnetic forces of attraction or repulsion, thus counteracting the gravitational force applied to that object [15, 16]. Nowadays, it is increasingly used in areas of passenger and cargo transportation because it drastically reduces the mechanical losses that conventional systemsentail [17]. However, systems that employ magnetic levitation often require a robust control algorithm as they are normally unstable and nonlinear [18; 19]. Magnetic suspension controlling a DC electromagnet is the most used method, from advanced land transport to contactless bearings for high and low speeds. This is a method that has been studied for over a century, but which is constantly improving due to technological advances in several areas such as power electronics, control theory, and mechanics [15; 17]. A similar magnetic levitation system is studied in [11], where the authors use a Nonlinear Autoregressive Moving Average (NARMA) neural network to perform the system identification and a neural network that learns the system dynamics, thus emulating its response to the desired input. The authors then use a neural network predictive controller to control the levitation system. Studies on the same system are conducted in [20], where a model reference controller is trained to control the system. In Reference [21], the authors propose an RBF ARX model based MPC strategy for the ball position control of a fast-response magnetic levitation system. The applied strategy worked like a time-varying locally linear ARX model-based linear MPC process. It was illustrated that the RBF-ARX-MPC is effective and feasible in modeling and controlling the fast-responding, strongly nonlinear, and open-loop unstable system. Work [22] presents an application of magnetic levitation to stabilization and tracking control of a single degree-of-freedom mass-spring-damper vibrating mechanical system. An output feedback control scheme based on differential flatness for global stabilization and asymptotic tracking tasks of some desired reference position trajectory is proposed. Experimental and simulation results showed the efficient and satisfactory performance of the tracking control scheme and the acceptable signal estimation. Other similar mechanisms such as air levitation systems are also considered in various works. In Reference [23], the control of an air levitation system with limited sensing is studied. It uses a sliding mode control, but it was modified to take only a measure of the position, which is the only one available.