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This paper deals with the problem of adaptive output regulation formultivariable nonlinear systems by presenting a learning-based adaptiveinternal model-based design strategy. The approach builds on the recentlyproposed adaptive internal model design techniques based on the theory ofnonlinear Luenberger observers, and the adaptation side is approached as aprobabilistic regression problem. In particular, Gaussian process priors areemployed to cope with the learning problem. Unlike the previous approaches inthe field, here only coarse assumptions about the friend structure arerequired, making the proposed approach suitable for applications where theexosystem is highly uncertain. The paper presents performance bounds on theattained regulation error and numerical simulations showing how the proposedmethod outperforms previous approaches.

Data-driven Output Regulation via Gaussian Processes and Luenberger Internal Models