Neural network model to control an experimental chaotic pendulum

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Abstract
A feedforward neural network was trained to predict the motion of an experimental, driven, and damped pendulum operating in a chaotic regime. The network learned the behavior of the pendulum from a time series of the pendulum’s angle, the single measured variable. The validity of the neural network model was assessed by comparing Poincaré sections of measured and model-generated data. The model was used to find unstable periodic orbits (UPO’s), up to period 7. Two selected orbits were stabilized using the semicontinuous control extension, as described by De Korte, Schouten, and van den Bleek [Phys. Rev. E 52, 3358 (1995)], of the well-known Ott-Grebogi-Yorke chaos control scheme [Phys. Rev. Lett. 64, 1196 (1990)]. The neural network was used as an alternative to local linear models. It has two advantages: (i) it requires much less data, and (ii) it can find many more UPO’s than those found directly from the measured time series. ©1996 The American Physical Society.