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Due to the increasing complexity of technical systems, accurate firstprinciple models can often not be obtained. Supervised machine learning canmitigate this issue by inferring models from measurement data. Gaussian processregression is particularly well suited for this purpose due to its highdata-efficiency and its explicit uncertainty representation, which allows thederivation of prediction error bounds. These error bounds have been exploitedto show tracking accuracy guarantees for a variety of control approaches, buttheir direct dependency on the training data is generally unclear. We addressthis 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 datadensity. Based on the prediction error bound, we prove time-varying trackingaccuracy guarantees for learned GP models used as feedback compensation ofunknown nonlinearities, and show to achieve vanishing tracking error withincreasing data density. This enables us to develop an episodic approach forlearning Gaussian process models, such that an arbitrary tracking accuracy canbe guaranteed. The effectiveness of the derived theory is demonstrated inseveral simulations.

Episodic Gaussian Process-Based Learning Control with Vanishing Tracking Errors