Control of an overhead crane: Stabilization of flexibilities

This paper deals with the feedback stabilization of the cable of an overhead crane, by the means of the position of the platform. The well-posedness of the closed-loop PDE system with boundary control and homogeneous Neumann condition on part of the boundary is established, the asymptotic stabilization is proved by Lasalle's Invariance Principle for a class of simple feedbacks and decay estimates are given. Illustrative simulations are displayed.