Physics-Informed Neural Networks (PINNs) offer a promising framework for solving differential problems, including Partial Differential Equations (PDEs) and Optimal Control Problems (OCPs). They have also been explored in parametric settings, which involves PDEs that depend on a set of parameters. In this context, the objective is to create a framework capable of efficiently generating numerical approximations of the solution when the parameter input of the differential problem changes. In fact, standard numerical methods can be too time-consuming to solve the problem in real-time and for many parameters. This thesis focuses on applying PINNs parametric OCPs. The first contribution is the improvement of the performances of standard PINNs on two test cases already investigated in the literature: a parametric Elliptic OCP and a parametric Stokes OCP.