Null Internal Controllability for a Kirchhoff–Love Plate with a Comb-Like Shaped Structure

This paper is devoted to studying the null internal controllability of a Kirchoff–Love thin plate with a middle surface having a comb-like shaped structure with a large number of thin fingers described by a small positive parameter \varepsilon . It is often impossible to directly approach such a problem numerically, due to the large number of thin fingers. So an asymptotic analysis is needed. In this paper, we first prove that the problem is null controllable at each level \varepsilon. We then prove that the sequence of the respective controls with minimal L^2 norm converges, as \varepsilon vanishes, to a limit control function ensuring the optimal null controllability of a degenerate limit problem set in a domain without fingers.