  Safety-critical technical systems operating in unknown environments require
the ability to quickly adapt their behavior, which can be achieved in control
by inferring a model online from the data stream generated during operation.
Gaussian process-based learning is particularly well suited for safety-critical
applications as it ensures bounded prediction errors. While there exist
computationally efficient approximations for online inference, these approaches
lack guarantees for the prediction error and have high memory requirements, and
are therefore not applicable to safety-critical systems with tight memory
constraints. In this work, we propose a novel networked online learning
approach based on Gaussian process regression, which addresses the issue of
limited local resources by employing remote data management in the cloud. Our
approach formally guarantees a bounded tracking error with high probability,
which is exploited to identify the most relevant data to achieve a certain
control performance. We further propose an effective data transmission scheme
between the local system and the cloud taking bandwidth limitations and time
delay of the transmission channel into account. The effectiveness of the
proposed method is successfully demonstrated in a simulation.
