We consider the problem of generating and tracking a trajectory between two arbitrary parabolic profiles of a periodic 2D channel flow, which is linearly unstable for high Reynolds numbers. Also known as the Poiseuille flow, this problem is frequently cited as a paradigm for
transition to turbulence. Our procedure consists in generating an exact trajectory of the nonlinear system that approaches exponentially
the objective profile. Using a backstepping method, we then design boundary control laws guaranteeing that the error between the state and the trajectory decays exponentially. The result is first proved for the linearized Stokes equations, then shown to hold locally for the nonlinear Navier-Stokes system.