  We present a straightforward and efficient way to control unstable robotic
systems using an estimated dynamics model. Specifically, we show how to exploit
the differentiability of Gaussian Processes to create a state-dependent
linearized approximation of the true continuous dynamics that can be integrated
with model predictive control. Our approach is compatible with most Gaussian
process approaches for system identification, and can learn an accurate model
using modest amounts of training data. We validate our approach by learning the
dynamics of an unstable system such as a segway with a 7-D state space and 2-D
input space (using only one minute of data), and we show that the resulting
controller is robust to unmodelled dynamics and disturbances, while
state-of-the-art control methods based on nominal models can fail under small
perturbations. Code is open sourced at
https://github.com/learning-and-control/core .
