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

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.