Failure of the Ott-Grebogi-York-type controllers for nonhyperbolic chaos

It is considered that nonhyperbolicity affects the achievement of Ott-Grebogi-York-type (OGY-type) controllers. The result shows that, without a priori analytical knowledge of the dynamics, it is impossible to estimate the local dynamics from an experimental time series due to the singularity of the corresponding least-squares problem which results from the nonhyperbolicity in the system. Thus, it is necessary to destroy chaos before obtaining the formation for attempting control by experimental time series. The result explains a physical experimental result in the failure of chaos control in a parametrically excited pendulum model.