Both methods require a previous determination of the unstable periodic orbits of the chaotic system before the controlling algorithm can be designed.
Edward Ott, Celso Grebogi and James A. Yorke were the first to make the key observation that the infinite number of unstable periodic orbits typically embedded in a chaotic attractor could be taken advantage of for the purpose of achieving control by means of applying only very small perturbations.
In the OGY method, small, wisely chosen, kicks are applied to the system once per cycle, to maintain it near the desired unstable periodic orbit.
One strength of this method is that it does not require a detailed model of the chaotic system but only some information about the Poincaré section.
[4] The weaknesses of this method are in isolating the Poincaré section and in calculating the precise perturbations necessary to attain stability.