  This paper deals with the problem of adaptive output regulation for
multivariable nonlinear systems by presenting a learning-based adaptive
internal model-based design strategy. The approach builds on the recently
proposed adaptive internal model design techniques based on the theory of
nonlinear Luenberger observers, and the adaptation side is approached as a
probabilistic regression problem. In particular, Gaussian process priors are
employed to cope with the learning problem. Unlike the previous approaches in
the field, here only coarse assumptions about the friend structure are
required, making the proposed approach suitable for applications where the
exosystem is highly uncertain. The paper presents performance bounds on the
attained regulation error and numerical simulations showing how the proposed
method outperforms previous approaches.
