  Nonlinear model predictive control (NMPC) is one of the few control methods
that can handle multivariable nonlinear controlsystems with constraints.
Gaussian processes (GPs) present a powerful tool to identify the required plant
model and quantifythe residual uncertainty of the plant-model mismatch. It is
crucial to consider this uncertainty, since it may lead to worsecontrol
performance and constraint violations. In this paper we propose a new method to
design a GP-based NMPC algorithmfor finite horizon control problems. The method
generates Monte Carlo samples of the GP offline for constraint tighteningusing
back-offs. The tightened constraints then guarantee the satisfaction of chance
constraints online. Advantages of our proposed approach over existing methods
include fast online evaluation, consideration of closed-loop behaviour, and
thepossibility to alleviate conservativeness by considering both online
learning and state dependency of the uncertainty. The algorithm is verified on
a challenging semi-batch bioprocess case study.
