  Data availability has dramatically increased in recent years, driving
model-based control methods to exploit learning techniques for improving the
system description, and thus control performance. Two key factors that hinder
the practical applicability of learning methods in control are their high
computational complexity and limited generalization capabilities to unseen
conditions. Meta-learning is a powerful tool that enables efficient learning
across a finite set of related tasks, easing adaptation to new unseen tasks.
This paper makes use of a meta-learning approach for adaptive model predictive
control, by learning a system model that leverages data from previous related
tasks, while enabling fast fine-tuning to the current task during closed-loop
operation. The dynamics is modeled via Gaussian process regression and,
building on the Karhunen-Lo{\`e}ve expansion, can be approximately reformulated
as a finite linear combination of kernel eigenfunctions. Using data collected
over a set of tasks, the eigenfunction hyperparameters are optimized in a
meta-training phase by maximizing a variational bound for the log-marginal
likelihood. During meta-testing, the eigenfunctions are fixed, so that only the
linear parameters are adapted to the new unseen task in an online adaptive
fashion via Bayesian linear regression, providing a simple and efficient
inference scheme. Simulation results are provided for autonomous racing with
miniature race cars adapting to unseen road conditions.
