Control of chaos using neural networks

A method is described for online closed-loop neural network control of chaotic systems. This control is achieved by presenting an artificial neural network with a desired reference trajectory and a chaotic carrier signal. Error backpropagation with threshold adaptation is used to learn the chaotic output, which is converted to the desired attracting motion using delay coordinate embedding techniques. Applying these techniques to a nonstationary error equation results in the formulation of the control perturbation which will drive the learned chaotic signal to the desired reference.