Adaptive fuzzy sliding mode control of a chaotic pendulum with noisy signals

Chaotic response is related to a dense set of unstable periodic orbits (UPOs) and the system often visits the neighborhood of each one of them. Moreover, chaos has sensitive dependence to initial conditions, which implies that the system evolution may be altered by small perturbations. Chaos control is based on the richness of chaotic behavior and may be understood as the use of tiny perturbations for the stabilization of an UPO enclosed in a chaotic attractor. It makes this kind of behavior to be desirable in a variety of applications, since one of these UPOs can provide better performance than others in a particular situation. In this work, an adaptive fuzzy sliding mode controller is combined with the close return method for the stabilization of UPOs in a chaotic pendulum. The adaptive fuzzy inference system is embedded in a smooth sliding mode controller to cope with both structured and unstructured uncertainties. Since noise contamination is unavoidable in experimental data acquisition, this work also investigates the effect of noisy signals on the used control law, verifying their influence on the system stabilization and on the required control action. Numerical results are presented in order to illustrate the ability of the proposed control scheme to track UPOs even in the presence of modeling inaccuracies and noisy input signals.