# Stochastic data-driven model predictive control using Gaussian processes

arXiv: https://arxiv.org/abs/1908.01786 · HTML: https://mlsanity.com/paper/1908.01786/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2019.

## Built on by (most cited first, 19 of 19)

- [Maximizing information from chemical engineering data sets: Applications to machine learning](https://mlsanity.com/paper/2201.10035/) (2022)
- [Safe Chance Constrained Reinforcement Learning for Batch Process Control](https://mlsanity.com/paper/2104.11706/) (2021)
- [Adaptive Stochastic Nonlinear Model Predictive Control with Look-ahead Deep Reinforcement Learning for Autonomous Vehicle Motion Control](https://mlsanity.com/paper/2311.04303/) (2023)
- [Towards safe and tractable Gaussian process-based MPC: Efficient sampling within a sequential quadratic programming framework](https://mlsanity.com/paper/2409.08616/) (2024)
- [Koopman-Equivariant Gaussian Processes](https://mlsanity.com/paper/2502.06645/) (2025)
- [Safe Real-Time Optimization using Multi-Fidelity Gaussian Processes](https://mlsanity.com/paper/2111.05589/) (2021)
- [Designing Robust Biotechnological Processes Regarding Variabilities using Multi-Objective Optimization Applied to a Biopharmaceutical Seed Train Design](https://mlsanity.com/paper/2205.03261/) (2022)
- [When Bioprocess Engineering Meets Machine Learning: A Survey from the Perspective of Automated Bioprocess Development](https://mlsanity.com/paper/2209.01083/) (2022)
- [Neural ODEs as Feedback Policies for Nonlinear Optimal Control](https://mlsanity.com/paper/2210.11245/) (2022)
- [Hybrid Gaussian Process Modeling Applied to Economic Stochastic Model Predictive Control of Batch Processes](https://mlsanity.com/paper/2108.06430/) (2021)
- [Survey and Tutorial of Reinforcement Learning Methods in Process Systems Engineering](https://mlsanity.com/paper/2510.24272/) (2025)
- [Combining Gaussian processes and polynomial chaos expansions for stochastic nonlinear model predictive control](https://mlsanity.com/paper/2103.05441/) (2021)
- [Omics-driven hybrid dynamic modeling of bioprocesses with uncertainty estimation](https://mlsanity.com/paper/2410.18864/) (2024)
- [Concurrent Learning Based Tracking Control of Nonlinear Systems using Gaussian Process](https://mlsanity.com/paper/2106.00910/) (2021)
- [A Stochastic Online Forecast-and-Optimize Framework for Real-Time Energy Dispatch in Virtual Power Plants under Uncertainty](https://mlsanity.com/paper/2309.08642/) (2023)
- [Online Constraint Tightening in Stochastic Model Predictive Control: A Regression Approach](https://mlsanity.com/paper/2310.02942/) (2023)
- [Data-Driven Prediction and Control of Hammerstein-Wiener Systems with Implicit Gaussian Processes](https://mlsanity.com/paper/2501.15849/) (2025)
- [Deep Kernel Bayesian Optimisation for Closed-Loop Electrode Microstructure Design with User-Defined Properties based on GANs](https://mlsanity.com/paper/2508.00833/) (2025)
- [Iterative Model-Learning Scheme via Gaussian Processes for Nonlinear Model Predictive Control of (Semi-)Batch Processes](https://mlsanity.com/paper/2604.22672/) (2026)

## Abstract (arXiv)

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.