Swinging up the Stephenson-Kapitza pendulum

We propose a novel vibrational control law for the Stephenson-Kapitza pendulum. The considered control law achieves practical asymptotic stabilization of the upper pendulum position and the region of attraction is large enough to swing up the pendulum. The control law includes a state dependent term that allows to approximate an L_gV control law in a time averaged sense. The control law is still of vibrational type and, in a neighborhood of the upper pendulum position, it coincides with the open-loop vibrational input as it is used in the Stephenson-Kapitza pendulum.