Control for Fast and Stable Laminar-to-High-Reynolds-Numbers Transfer in a 2D

(Communicated by Shouhong Wang) Abstract. 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 sys-tem that approaches exponentially the objective profile. Using a backstepping method, we then design boundary control laws guaranteeing that the error be-tween the state and the trajectory decays exponentially in L2, H1, and H2 norms. The result is first proved for the linearized Stokes equations, then shown to hold locally for the nonlinear Navier-Stokes system. 1. Introduction. On