Controlling chaos with a neural network

Chaotic situations may occur in complex systems as a normal operating mode or may accidentally be induced due to a change in some system parameter. The author reports one approach to the use of feedforward networks to dampen chaotic oscillations in Duffing´s oscillator. A catastrophic failure of the neural network controller is also studied. For networks with a single hidden layer, a point of diminishing returns was encountered as the size of the hidden layer increased. Suppression improves slightly as the hidden layer size increases. The larger networks take longer to train and are less responsive to changes in oscillator dynamics; however the larger networks recover faster after a transient disturbance in the oscillator dynamics. The majority of the tests were conducted on a network with a single hidden layer of 50 elements. The addition of more hidden layers provided only marginal improvements in suppression at the expense of much longer training times