Local exact controllability to the trajectories of the Swift–Hohenberg equation

This paper is addressed to study the local exact controllability to the trajectories of the Swift–Hohenberg equation. We first establish a new global Carleman estimate for the fourth order parabolic operator, and we consider the exact controllability to the trajectories of the linearized system. Then, by Local inversion theorem, we show that the same result holds for the Swift–Hohenberg equation.