  Robust controllers ensure stability in feedback loops designed under
uncertainty but at the cost of performance. Model uncertainty in time-invariant
systems can be reduced by recently proposed learning-based methods, which
improve the performance of robust controllers using data. However, in practice,
many systems also exhibit uncertainty in the form of changes over time, e.g.,
due to weight shifts or wear and tear, leading to decreased performance or
instability of the learning-based controller. We propose an event-triggered
learning algorithm that decides when to learn in the face of uncertainty in the
LQR problem with rare or slow changes. Our key idea is to switch between robust
and learned controllers. For learning, we first approximate the optimal length
of the learning phase via Monte-Carlo estimations using a probabilistic model.
We then design a statistical test for uncertain systems based on the
moment-generating function of the LQR cost. The test detects changes in the
system under control and triggers re-learning when control performance
deteriorates due to system changes. We demonstrate improved performance over a
robust controller baseline in a numerical example.
