Episodic Gaussian Process-Based Learning Control with Vanishing Tracking
  Errors
Armin Lederer Jonas Umlauft Sandra Hirche
Due to the increasing complexity of technical systems, accurate first
principle models can often not be obtained. Supervised machine learning can
mitigate this issue by inferring models from measurement data. Gaussian process
regression is particularly well suited for this purpose due to its high
data-efficiency and its explicit uncertainty representation, which allows the
derivation of prediction error bounds. These error bounds have been exploited
to show tracking accuracy guarantees for a variety of control approaches, but
their direct dependency on the training data is generally unclear. We address
this issue by deriving a Bayesian prediction error bound for GP regression,
which we show to decay with the growth of a novel, kernel-based measure of data
density. Based on the prediction error bound, we prove time-varying tracking
accuracy guarantees for learned GP models used as feedback compensation of
unknown nonlinearities, and show to achieve vanishing tracking error with
increasing data density. This enables us to develop an episodic approach for
learning Gaussian process models, such that an arbitrary tracking accuracy can
be guaranteed. The effectiveness of the derived theory is demonstrated in
several simulations.