# Constrained Gaussian Process Learning for Model Predictive Control

arXiv: https://arxiv.org/abs/1911.10809 · HTML: https://mlsanity.com/paper/1911.10809/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2019.

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

- [Advanced Stationary and Non-Stationary Kernel Designs for Domain-Aware Gaussian Processes](https://mlsanity.com/paper/2102.03432/) (2021)
- [Gaussian Processes with State-Dependent Noise for Stochastic Control](https://mlsanity.com/paper/2305.16229/) (2023)

## Abstract (arXiv)

Many control tasks can be formulated as a tracking problem of a known or unknown reference signal. Examples are movement compensation in collaborative robotics, the synchronisation of oscillations for power systems or reference tracking of recipes in chemical process operation. Tracking performance as well as guaranteeing stability of the closed loop strongly depends on two factors: Firstly, it depends on whether the future desired tracking reference signal is known and, secondly, whether the system can track the reference at all. This paper shows how to use machine learning, i.e. Gaussian processes, to learn a reference from (noisy) data, while guaranteeing trackability of the modified desired reference predictions in the framework of model predictive control. Guarantees are provided by adjusting the hyperparameters via a constrained optimization. Two specific scenarios, i.e. asymptotically constant and periodical references, are discussed.