A new family of smooth strategies for swinging up a pendulum

In English The paper presents a new family of strategies for swinging up a pendulum. They are derived from physical arguments based on two ideas: shaping the Hamiltonian for a system without damping; and providing damping or energy pumping in relevant regions. A two-parameter family of simple strategies without switches with nice properties is obtained. The main result is that all solutions that do not start at a zero Lebesgue measure set will converge to the upright position for a wide range of the parameters in the control law. Thus, the swing-up and the stabilization problems are simultaneously solved with a single, smooth law.