# Stochastic data-driven model predictive control using Gaussian processes

## TL;DR

This paper introduces a Gaussian process-based stochastic model predictive control method that accounts for uncertainty, ensuring constraint satisfaction and improved performance in nonlinear control systems.

## Contribution

It proposes a novel GP-based NMPC algorithm with offline Monte Carlo sampling for constraint tightening, enhancing online evaluation speed and handling uncertainty more effectively.

## Key findings

- Successfully applied to a semi-batch bioprocess case study.
- Guarantees chance constraint satisfaction through offline Monte Carlo sampling.
- Reduces conservativeness by combining online learning with state-dependent uncertainty.

## Abstract

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.