# Cautious Model Predictive Control using Gaussian Process Regression

arXiv: https://arxiv.org/abs/1705.10702 · HTML: https://mlsanity.com/paper/1705.10702/

## Key facts

- Cited by 91 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2017.

## Built on by (most cited first, 30 of 91)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [A Review of Safe Reinforcement Learning: Methods, Theory and Applications](https://mlsanity.com/paper/2205.10330/) (2022)
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- [safe-control-gym: a Unified Benchmark Suite for Safe Learning-based Control and Reinforcement Learning in Robotics](https://mlsanity.com/paper/2109.06325/) (2021)
- [Context-Aware Safe Reinforcement Learning for Non-Stationary Environments](https://mlsanity.com/paper/2101.00531/) (2021)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classification](https://mlsanity.com/paper/2502.02133/) (2025)
- [Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applications](https://mlsanity.com/paper/2109.02606/) (2021)
- [Physically Consistent Neural Networks for building thermal modeling: theory and analysis](https://mlsanity.com/paper/2112.03212/) (2021)
- [Robust Control for Dynamical Systems With Non-Gaussian Noise via Formal Abstractions](https://mlsanity.com/paper/2301.01526/) (2023)
- [Robust Uncertainty Bounds in Reproducing Kernel Hilbert Spaces: A Convex Optimization Approach](https://mlsanity.com/paper/2104.09582/) (2021)
- [On Recurrent Neural Networks for learning-based control: recent results and ideas for future developments](https://mlsanity.com/paper/2111.13557/) (2021)
- [Single Image Depth Prediction Made Better: A Multivariate Gaussian Take](https://mlsanity.com/paper/2303.18164/) (2023)
- [Sampling-Based Robust Control of Autonomous Systems with Non-Gaussian Noise](https://mlsanity.com/paper/2110.12662/) (2021)
- [Active Learning of Discrete-Time Dynamics for Uncertainty-Aware Model Predictive Control](https://mlsanity.com/paper/2210.12583/) (2022)
- [Improved uncertainty quantification for neural networks with Bayesian last layer](https://mlsanity.com/paper/2302.10975/) (2023)
- [SafeAPT: Safe Simulation-to-Real Robot Learning using Diverse Policies Learned in Simulation](https://mlsanity.com/paper/2201.13248/) (2022)
- [SkyJEPA: Learning Long-Horizon World Models for Zero-Shot Sim-to-Real Control of Quadrotors](https://mlsanity.com/paper/2606.23444/) (2026)
- [Machine learning for industrial sensing and control: A survey and practical perspective](https://mlsanity.com/paper/2401.13836/) (2024)
- [Safe Guaranteed Exploration for Non-linear Systems](https://mlsanity.com/paper/2402.06562/) (2024)
- [Stability-informed Bayesian Optimization for MPC Cost Function Learning](https://mlsanity.com/paper/2404.12187/) (2024)
- [Adaptive Robust Model Predictive Control with Matched and Unmatched Uncertainty](https://mlsanity.com/paper/2104.08261/) (2021)
- [Event-Triggered Model Predictive Control with Deep Reinforcement Learning for Autonomous Driving](https://mlsanity.com/paper/2208.10302/) (2022)
- [Safe and Stable Closed-Loop Learning for Neural-Network-Supported Model Predictive Control](https://mlsanity.com/paper/2409.10171/) (2024)
- [Real-Time Decision-Making for Digital Twin in Additive Manufacturing with Model Predictive Control using Time-Series Deep Neural Networks](https://mlsanity.com/paper/2501.07601/) (2025)
- [C-MCTS: Safe Planning with Monte Carlo Tree Search](https://mlsanity.com/paper/2305.16209/) (2023)
- [Towards safe and tractable Gaussian process-based MPC: Efficient sampling within a sequential quadratic programming framework](https://mlsanity.com/paper/2409.08616/) (2024)
- [Safe Exploration via Policy Priors](https://mlsanity.com/paper/2601.19612/) (2026)
- [Finite-Sample-Based Reachability for Safe Control with Gaussian Process Dynamics](https://mlsanity.com/paper/2505.07594/) (2025)
- [Probabilistic Robust Linear Quadratic Regulators with Gaussian Processes](https://mlsanity.com/paper/2105.07668/) (2021)

## Abstract (arXiv)

Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for modeling of nonlinear dynamical systems from data, as it allows the direct assessment of residual model uncertainty. We present a model predictive control (MPC) approach that integrates a nominal system with an additive nonlinear part of the dynamics modeled as a GP. Approximation techniques for propagating the state distribution are reviewed and we describe a principled way of formulating the chance constrained MPC problem, which takes into account residual uncertainties provided by the GP model to enable cautious control. Using additional approximations for efficient computation, we finally demonstrate the approach in a simulation example, as well as in a hardware implementation for autonomous racing of remote controlled race cars, highlighting improvements with regard to both performance and safety over a nominal controller.