Sliding-mode control of a chaotic pendulum: stabilization and targeting of an unstable periodic orbit

Using linear methods, both a stabilizing and a targeting controller have to be designed to control a chaotic system on an unstable periodic orbit. In this paper, it is shown that by applying a sliding-mode controller stabilization and targeting of periodic orbits can be achieved simultaneously. Sliding-mode controllers are nonlinear controllers. Systems controlled by sliding-mode controllers exhibit robust behavior towards model uncertainties and noise. The proposed method is proven to be suitable for chaotic systems even in the presence of model uncertainties and noise. To prevent chattering and to increase robustness, the hyperbolic tangent is applied within the boundary layer of the sliding-mode controller. The analysis is illustrated for the harmonically driven damped pendulum.