Exact boundary controllability of a nonlinear shallow spherical shell
We consider the problem of boundary exact controllability of a coupled nonlinear system which describes vibrations of a thin, shallow, spherical shell. We show that under the geometric condition of "shallowness", which restricts the curvature with respect to the thickness, the system is exactly controllable in the natural "finite energy" space by means of L2 controls. This controllability is produced via moments and shear forces applied to the edge of the shell.
Mathematical Models and Methods in Applied Sciences
Bradley, M., & Lasiecka, I. (1998). Exact boundary controllability of a nonlinear shallow spherical shell. Mathematical Models and Methods in Applied Sciences, 8 (6), 927-955. https://doi.org/10.1142/S0218202598000421