In this work, we combine nonlinear system control techniques with
next-generation reservoir computing, a best-in-class machine learning approach
for predicting the behavior of dynamical systems. We demonstrate the
performance of the controller in a series of control tasks for the chaotic
H\'enon map, including controlling the system between unstable fixed-points,
stabilizing the system to higher order periodic orbits, and to an arbitrary
desired state. We show that our controller succeeds in these tasks, requires
only 10 data points for training, can control the system to a desired
trajectory in a single iteration, and is robust to noise and modeling error.Comment: 9 pages, 8 figure