Analysis of the energy based control for swinging up two pendulums

This paper studies the energy based control for swinging up two pendulums on a cart. This paper presents an original and detail analysis of the convergence of the energies of two pendulums and provides the condition such that the pendulums can be swung up. Moreover, the stability analysis of the motion of two pendulums under the energy based control is accomplished via the concept of stability of an invariant set. These analyses not only show theoretically the effectiveness of the energy based control for swinging up two pendulums, but also pave one way for analyzing and designing the energy based control for more complicated underactuated mechanical systems.