Exact controllability and asymptotic limit for thin plates

We consider the exact controllability problem for a three-dimensional linear elastic thin plate, with thickness 2ε and a polygonal middle surface. Controls are imposed on the lateral surface and at the top and bottom of the plate. The asymptotic limit when ε→0 is computed. We obtain that the displacements converge to a controlled Kirchhoff–Love displacement, where the normal displacement satisfies the usual two-dimensional evolution equation for a linear plate, with controls on the boundary and in the interior of the plate.