Adaptive control of dynamical systems using reservoir computing

We demonstrate a data-driven technique for adaptive control of dynamical systems that exploits the reservoir computing method. We show that a reservoir computer can be trained to predict a system parameter from the time series. Subsequently, a control signal based on the predicted parameter can be used as a feedback to the dynamical system to lead it to a target state. Our results show that the dynamical system can be controlled throughout a wide range of attractor types. One set of training data consisting of only a few time series corresponding to the known parameter values enables our scheme to control a dynamical system to an arbitrary target attractor starting from any other initial attractor. In addition to numerical results, we implement our scheme in real-world systems, such as a Rössler system, realized in an electronic circuit to demonstrate the effectiveness of our approach.