# A Tutorial on Gaussian Process Learning-based Model Predictive Control

arXiv: https://arxiv.org/abs/2404.03689 · HTML: https://mlsanity.com/paper/2404.03689/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 38 references that are in the map.
- First posted on arXiv 2 Apr 2024.

## Builds on (most cited first, 10 of 10)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [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)
- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [An Intuitive Tutorial to Gaussian Process Regression](https://mlsanity.com/paper/2009.10862/) (2020)
- [Cautious NMPC with Gaussian Process Dynamics for Autonomous Miniature Race Cars](https://mlsanity.com/paper/1711.06586/) (2017)
- [Improving safety in mixed traffic: A learning-based model predictive control for autonomous and human-driven vehicle platooning](https://mlsanity.com/paper/2211.04665/) (2022)
- [Learning-Based Modeling of Human-Autonomous Vehicle Interaction for Improved Safety in Mixed-Vehicle Platooning Control](https://mlsanity.com/paper/2303.09452/) (2023)

## Built on by (most cited first, 1 of 1)

- [T2S-MPC: Time-Embedded Online Adaptive Model Predictive Control for Time-Varying Dynamics](https://mlsanity.com/paper/2605.24852/) (2026)

## Abstract (arXiv)

This tutorial provides a systematic introduction to Gaussian process learning-based model predictive control (GP-MPC), an advanced approach integrating Gaussian process (GP) with model predictive control (MPC) for enhanced control in complex systems. It begins with GP regression fundamentals, illustrating how it enriches MPC with enhanced predictive accuracy and robust handling of uncertainties. A central contribution of this tutorial is the first detailed, systematic mathematical formulation of GP-MPC in literature, focusing on deriving the approximation of means and variances propagation for GP multi-step predictions. Practical applications in robotics control, such as path-following for mobile robots in challenging terrains and mixed-vehicle platooning, are discussed to demonstrate the real-world effectiveness and adaptability of GP-MPC. This tutorial aims to make GP-MPC accessible to researchers and practitioners, enriching the learning-based control field with in-depth theoretical and practical insights and fostering further innovations in complex system control.