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We develop a three-component Model Predictive Control (MPC) algorithm toachieve output-reference tracking with prescribed performance forcontinuous-time nonlinear systems. One component is so-called funnel MPC, whichachieves reference tracking with prescribed performance for the model outputfor suitable models. Recently, this MPC algorithm has been combined with amodel-free reactive feedback controller (second component) to account formodel-plant mismatches, bounded disturbances, and uncertainties. Byconstruction, this two-component controller defines a robust funnel MPCalgorithm. It achieves output-reference tracking within prescribed bounds onthe tracking error for a class of unknown nonlinear systems. In this paper, weextend the robust funnel MPC by a machine learning component to adapt theunderlying model to the system data and, thus, improve the contribution of MPC.We derive sufficient structural conditions to define a class of models forfunnel MPC, and provide a characterization of suitable learning schemes. Sincerobust funnel MPC is inherently robust and the evolution of the tracking errorin the prescribed performance funnel is guaranteed, the additional learningcomponent is able to perform the learning task online -- even without aninitial model or offline training.

Safe continual learning in model predictive control with prescribed bounds on the tracking error