LbMATMPC: an open-source toolbox for Gaussian Process modeling within Learning-based Nonlinear Model Predictive Control

In the last years, Nonlinear Model Predictive Control (NMPC) has widely spread both in research and industrial contexts. NMPC reliability, however, depends on the accuracy of the model description, that can be subject to considerable uncertainty. On the other hand, advances in the machine learning techniques led to a renewed interest in data-driven control strategies for complex systems, defining a novel research field, namely Learning-based NMPC. In this manuscript, we present an open-source toolbox that combines MATMPC (a MATLAB-based Fast NMPC solver) and gpr-pytorch (a Python library for Gaussian Process (GP) regression) to define an off-the-shelves framework for implementation of GP-based Learning-based NMPC. Starting from a nominal model and model mismatch data or input-output measurements, the toolbox allows to train the GP either as model mismatch estimator or black-box model and get automatically the information needed for the NMPC problem. An example of usage in an experimental scenario for the control of a Furuta pendulum is presented, and a Monte Carlo analysis is carried out in a simulative scenario.