The primary objective of this master's thesis project is the software implementation and the test of the performances of a novel control-based optimization algorithm, referred to as feedback linearization controlled multiplier, applied to the training of a specific category of recurrent neural networks (RNNs) known as Output Error Neural Networks (NNOE). The final goal is to construct mathematical models from sequential data and capture temporal dependencies between input and output measurements. We implement the algorithm in both Python and MATLAB to assess various performance aspects, address critical issues, and evaluate the efficiency of GPU utilization. We experiment with various Python’s libraries such as PyTorch, TensorFlow, and NumPy, concluding that PyTorch provides the best performances.