A remarkable feature of the control method developed by Ott, Grebogi, and Yorke is that it can be applied in situations where no underlying model is known. |

Often experimental data are sufficient to extract the information necessary for exercising control. |

In experiments, we measure some variable, x, of the system at
fixed time intervals. Call the measured values x_{1}, x_{2},
x_{3}, ... . |

To locate a fixed point, we plot the return map,
x_{n+1} vs x_{n}, and look for where the return map crosses the
diagonal. |

To locate and stabilize a 2-cycle, use the second return map
(plot x_{n+2} vs x_{n}), and then the same strategy can be applied.
The same idea works for longer cycles as well. |

The OGY method works this way. |

Return to Control of Chaos.