This thesis is a satellite continuation to [4] in which the authors introduce a technique to solve equality constrained minimization problems (such as the training of a Re- current Neural Network) via a modified version of the standard gradient algorithm, generating a fictitious system that is controlled with the Lagrange multipliers of the problem and has the constraints violation as its output. Their work introduces two control strategies. The first one consists in using a PI controller, while the second employs feedback linearization to define the lagrange multipliers vector in such a way that makes possible to directly push the constraint violation towards zero using the derivative of the constraints as input.