System identification for the Ott-Grebogi-Yorke controller design

A technique to compute the linearized Poincare map and the sensitivity vector required for the implementation of an Ott-Grebogi-Yorke (OGY) controller from experimental data is presented. Unlike previous methods, the linearized map and the sensitivity vector are computed using only data collected over a single period of the limit cycle. The main advantage of the present method is the fact that it eliminates the long waiting period required to design an OGY controller using previously known methods. Numerical examples are presented using the Duffing oscillator with random perturbations to simulate noisy experimental data.