  We present a straightforward and efficient way to estimate dynamics models
for unstable robotic systems. Specifically, we show how to exploit the
differentiability of Gaussian processes to create a state-dependent linearized
approximation of the true continuous dynamics. 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 iteratively learning the system dynamics of an unstable system such as a 9-D
segway (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.
