Stochastic data-driven model predictive control using Gaussian processes

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.