Suppressing unknown disturbances to dynamical systems using machine learning

Identifying and suppressing unknown disturbances to dynamical systems is a problem with applications in many different fields. In this Letter, we present a model-free method to identify and suppress an unknown disturbance to an unknown system based only on previous observations of the system under the influence of a known forcing function. We find that, under very mild restrictions on the training function, our method is able to robustly identify and suppress a large class of unknown disturbances. We illustrate our scheme with the identification of unknown forcings to an analog electric chaotic circuit and with a numerical example where a chaotic disturbance to the Lorenz system is identified and suppressed.