# Towards safe and tractable Gaussian process-based MPC: Efficient sampling within a sequential quadratic programming framework

arXiv: https://arxiv.org/abs/2409.08616 · HTML: https://mlsanity.com/paper/2409.08616/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 13 Sep 2024.

## Builds on (most cited first, 14 of 14)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [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)
- [acados: a modular open-source framework for fast embedded optimal control](https://mlsanity.com/paper/1910.13753/) (2019)
- [Linear model predictive safety certification for learning-based control](https://mlsanity.com/paper/1803.08552/) (2018)
- [Sampling from Gaussian Process Posteriors using Stochastic Gradient Descent](https://mlsanity.com/paper/2306.11589/) (2023)
- [Stochastic data-driven model predictive control using Gaussian processes](https://mlsanity.com/paper/1908.01786/) (2019)
- [On Simulation and Trajectory Prediction with Gaussian Process Dynamics](https://mlsanity.com/paper/1912.10900/) (2019)
- [Prediction with Approximated Gaussian Process Dynamical Models](https://mlsanity.com/paper/2006.14551/) (2020)
- [Gaussian Process Model Predictive Control of An Unmanned Quadrotor](https://mlsanity.com/paper/1707.04515/) (2017)
- [KPC: Learning-Based Model Predictive Control with Deterministic Guarantees](https://mlsanity.com/paper/2011.11303/) (2020)
- [Zero-Order Optimization for Gaussian Process-based Model Predictive Control](https://mlsanity.com/paper/2211.15522/) (2022)
- [Hybrid Gaussian Process Modeling Applied to Economic Stochastic Model Predictive Control of Batch Processes](https://mlsanity.com/paper/2108.06430/) (2021)

## Built on by (most cited first, 6 of 6)

- [Safe Exploration via Policy Priors](https://mlsanity.com/paper/2601.19612/) (2026)
- [Safe and Near-Optimal Control with Online Dynamics Learning](https://mlsanity.com/paper/2509.16650/) (2025)
- [A robust and adaptive MPC formulation for Gaussian process models](https://mlsanity.com/paper/2507.02098/) (2025)
- [Sampling-Based Safe Reinforcement Learning](https://mlsanity.com/paper/2605.19469/) (2026)
- [Directional Constraints for Efficient Exploration in Safe Reinforcement Learning](https://mlsanity.com/paper/2607.12784/) (2026)
- [Event-triggered Control and Online Learning for Networked Systems under Computational Delays](https://mlsanity.com/paper/2608.29576/) (2026)

## Abstract (arXiv)

Learning uncertain dynamics models using Gaussian process~(GP) regression has been demonstrated to enable high-performance and safety-aware control strategies for challenging real-world applications. Yet, for computational tractability, most approaches for Gaussian process-based model predictive control (GP-MPC) are based on approximations of the reachable set that are either overly conservative or impede the controller's safety guarantees. To address these challenges, we propose a robust GP-MPC formulation that guarantees constraint satisfaction with high probability. For its tractable implementation, we propose a sampling-based GP-MPC approach that iteratively generates consistent dynamics samples from the GP within a sequential quadratic programming framework. We highlight the improved reachable set approximation compared to existing methods, as well as real-time feasible computation times, using two numerical examples.