One of the main hypothesis made in variational data assimilation is to consider that the model is a strong constraint of the minimization i.e. that the model describes exactly the behavior of the system. Obviously the hypothesis is never respected. We propose here an alternative to the 4D-Var that takes into account model errors adding a non physical term into the model equation and controlling this term. A practical application is proposed on a simple case and a reduction of the size of control using preferred directions is introduced to make the method affordable for realistic applications.