Finite-time stabilization of an overhead crane with a flexible cable

Abstract

The paper is concerned with the finite-time stabilization of a hybrid PDE-ODE system which may serve as a model for the motion of an overhead crane with a flexible cable. The dynamics of the flexible cable is assumed to be described by the wave equation with constant coefficients. Using a nonlinear feedback law inspired by those given by Haimo in [12] for a second-order ODE, we prove that a finite-time stabilization occurs for the full system platform + cable. The global well-posedness of the system is also established by using the theory of nonlinear semigroups.