Data assimilation problems consist in retrieving the value of the solution at some time (everywhere in the domain) for an evolution problem knowing informations on the solution on a subdomain during a period of time. Data assimilation problems consist in retrieving the value of the solution at some time (everywhere in the domain) for an evolution problem knowing informations on the solution on a subdomain during a period of time. In a classical approach one tries to find the initial data using a Tychonov regularisation. This depnds on a regularisation parameter and the problem becomes ill-posed when this parameter tends to zero. We will present a non standard approach, based on Controllability techniques, which enables to retrieve the solution at the final time. A consequence is also to give a sense to the classical approach in a non standard functional class. We will present this on a heat equation or on a linearized Navier-Stokes system.