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

Abstract

We develop a three-component Model Predictive Control (MPC) algorithm to achieve output-reference tracking with prescribed performance for continuous-time nonlinear systems. One component is so-called funnel MPC, which achieves reference tracking with prescribed performance for the model output for suitable models. Recently, this MPC algorithm has been combined with a model-free reactive feedback controller (second component) to account for model-plant mismatches, bounded disturbances, and uncertainties. By construction, this two-component controller defines a robust funnel MPC algorithm. It achieves output-reference tracking within prescribed bounds on the tracking error for a class of unknown nonlinear systems. In this paper, we extend the robust funnel MPC by a machine learning component to adapt the underlying model to the system data and, thus, improve the contribution of MPC. We derive sufficient structural conditions to define a class of models for funnel MPC, and provide a characterization of suitable learning schemes. Since robust funnel MPC is inherently robust and the evolution of the tracking error in the prescribed performance funnel is guaranteed, the additional learning component is able to perform the learning task online -- even without an initial model or offline training.