Controlling chaos using nonlinear approximations for a pendulum with feedforward and feedback control

The OGY method is one of the most powerful techniques for controlling chaotic dynamical systems, but often requires very long time for stabilization of the targets. Recently, it was shown that the problem can be improved by using nonlinear approximations for the chaotic dynamical systems and the stable manifolds of the targets. We consider a pendulum with feedforward and feedback control and apply the improved method to the associated Poincare map. The derivatives of the Poincare map, which are necessary for application of the method, are computed by solving certain differential equations. Numerical examples are given and the effectiveness of the control method is demonstrated.