# Hybrid Gaussian Process Modeling Applied to Economic Stochastic Model Predictive Control of Batch Processes

arXiv: https://arxiv.org/abs/2108.06430 · HTML: https://mlsanity.com/paper/2108.06430/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 57 references that are in the map.
- First posted on arXiv 14 Aug 2021.

## Builds on (most cited first, 9 of 9)

- [Learning-based Model Predictive Control for Safe Exploration](https://mlsanity.com/paper/1803.08287/) (2018)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC](https://mlsanity.com/paper/1306.2861/) (2013)
- [Stochastic data-driven model predictive control using Gaussian processes](https://mlsanity.com/paper/1908.01786/) (2019)
- [Learning-based Model Predictive Control for Safe Exploration and Reinforcement Learning](https://mlsanity.com/paper/1906.12189/) (2019)
- [Cautious NMPC with Gaussian Process Dynamics for Autonomous Miniature Race Cars](https://mlsanity.com/paper/1711.06586/) (2017)
- [Gaussian Process Latent Force Models for Learning and Stochastic Control of Physical Systems](https://mlsanity.com/paper/1709.05409/) (2017)
- [Gaussian Process Model Predictive Control of An Unmanned Quadrotor](https://mlsanity.com/paper/1707.04515/) (2017)
- [Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints](https://mlsanity.com/paper/1410.4535/) (2014)

## Built on by (most cited first, 2 of 2)

- [Towards safe and tractable Gaussian process-based MPC: Efficient sampling within a sequential quadratic programming framework](https://mlsanity.com/paper/2409.08616/) (2024)
- [Stochastic Model Predictive Control Utilizing Bayesian Neural Networks](https://mlsanity.com/paper/2303.14519/) (2023)

## Abstract (arXiv)

Nonlinear model predictive control (NMPC) is an efficient approach for the control of nonlinear multivariable dynamic systems with constraints, which however requires an accurate plant model. Plant models can often be determined from first principles, parts of the model are however difficult to derive using physical laws alone. In this paper a hybrid Gaussian process (GP) first principles modeling scheme is proposed to overcome this issue, which exploits GPs to model the parts of the dynamic system that are difficult to describe using first principles. GPs not only give accurate predictions, but also quantify the residual uncertainty of this model. It is vital to account for this uncertainty in the control algorithm, to prevent constraint violations and performance deterioration. Monte Carlo samples of the GPs are generated offline to tighten constraints of the NMPC to ensure joint probabilistic constraint satisfaction online. Advantages of our method include fast online evaluation times, possibility to account for online learning alleviating conservativeness, and exploiting the flexibility of GPs and the data efficiency of first principle models. The algorithm is verified on a case study involving a challenging semi-batch bioreactor.