CHAOS IN A PENDULUM WITH FEEDBACK-CONTROL

We study chaotic dynamics of a pendulum subjected to linear feedback c ontrol with periodic desired motions. The pendulum is assumed to be dr iven by a servo-motor with small inductance, so that the feedback cont rol system reduces to a periodic perturbation of a planar Hamiltonian system. This Hamiltonian system can possess multiple saddle points wit h non-transverse homoclinic and/or heteroclinic orbits. Using Melnikov 's method, we obtain criteria for the existence of chaos in the pendul um motion. The computation of the Melnikov functions is performed by a numerical method. Several numerical examples are given and the theore tical predictions are compared with numerical simulation results for t he behavior of invariant manifolds.