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 x1, x2, x3, ... . |
To locate a fixed point, we plot the return map, xn+1 vs xn, and look for where the return map crosses the diagonal. |
To locate and stabilize a 2-cycle, use the second return map (plot xn+2 vs xn), 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.