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.