mlsanityData to 7 Oct 2026

Cautious Model Predictive Control using Gaussian Process Regression

arXiv 1705.10702 ↗First posted 30 May 2017eess.SY cs.SY math.OCcited by 91

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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.

Key facts. Cited by 91 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 May 2017.

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Citing papers per year: 2021: 19; 2022: 14; 2023: 18; 2024: 14; 2025: 11; 2026: 15.

91 papers.

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  1. 2021Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learningcited by 337
  2. 2022A Review of Safe Reinforcement Learning: Methods, Theory and Applicationscited by 169
  3. 2021Learning to Synthesize Programs as Interpretable and Generalizable Policiescited by 59
  4. 2021safe-control-gym: a Unified Benchmark Suite for Safe Learning-based Control and Reinforcement Learning in Roboticscited by 42
  5. 2021Context-Aware Safe Reinforcement Learning for Non-Stationary Environmentscited by 33
  6. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  7. 2025Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classificationcited by 19
  8. 2021Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applicationscited by 17
  9. 2021Physically Consistent Neural Networks for building thermal modeling: theory and analysiscited by 16
  10. 2023Robust Control for Dynamical Systems With Non-Gaussian Noise via Formal Abstractionscited by 16
  11. 2021Robust Uncertainty Bounds in Reproducing Kernel Hilbert Spaces: A Convex Optimization Approachcited by 14
  12. 2021On Recurrent Neural Networks for learning-based control: recent results and ideas for future developmentscited by 14
38 more
  1. 2023Single Image Depth Prediction Made Better: A Multivariate Gaussian Takecited by 14
  2. 2021Sampling-Based Robust Control of Autonomous Systems with Non-Gaussian Noisecited by 13
  3. 2022Active Learning of Discrete-Time Dynamics for Uncertainty-Aware Model Predictive Controlcited by 13
  4. 2023Improved uncertainty quantification for neural networks with Bayesian last layercited by 11
  5. 2022SafeAPT: Safe Simulation-to-Real Robot Learning using Diverse Policies Learned in Simulationcited by 10
  6. 2026SkyJEPA: Learning Long-Horizon World Models for Zero-Shot Sim-to-Real Control of Quadrotorscited by 9
  7. 2024Safe Guaranteed Exploration for Non-linear Systemscited by 8
  8. 2024Stability-informed Bayesian Optimization for MPC Cost Function Learningcited by 8
  9. 2021Adaptive Robust Model Predictive Control with Matched and Unmatched Uncertaintycited by 7
  10. 2025Real-Time Decision-Making for Digital Twin in Additive Manufacturing with Model Predictive Control using Time-Series Deep Neural Networkscited by 7
  11. 2022Event-Triggered Model Predictive Control with Deep Reinforcement Learning for Autonomous Drivingcited by 6
  12. 2023C-MCTS: Safe Planning with Monte Carlo Tree Searchcited by 6
  13. 2024Machine learning for industrial sensing and control: A survey and practical perspectivecited by 6
  14. 2024Towards safe and tractable Gaussian process-based MPC: Efficient sampling within a sequential quadratic programming frameworkcited by 6
  15. 2024Safe and Stable Closed-Loop Learning for Neural-Network-Supported Model Predictive Controlcited by 6
  16. 2026Safe Exploration via Policy Priorscited by 6
  17. 2025Finite-Sample-Based Reachability for Safe Control with Gaussian Process Dynamicscited by 5
  18. 2021Probabilistic Robust Linear Quadratic Regulators with Gaussian Processescited by 4
  19. 2022Learning Stochastic Parametric Differentiable Predictive Control Policiescited by 4
  20. 2022Neural Solvers for Fast and Accurate Numerical Optimal Controlcited by 4
  21. 2022Zero-Order Optimization for Gaussian Process-based Model Predictive Controlcited by 4
  22. 2022Model Predictive Robustness of Signal Temporal Logic Predicatescited by 3
  23. 2023Safe Machine-Learning-supported Model Predictive Force and Motion Control in Roboticscited by 3
  24. 2024Random Features Approximation for Control-Affine Systemscited by 3
  25. 2021Hybrid Gaussian Process Modeling Applied to Economic Stochastic Model Predictive Control of Batch Processescited by 2
  26. 2022An Offset-Free Nonlinear MPC scheme for systems learned by Neural NARX modelscited by 2
  27. 2022Data-Driven Stochastic AC-OPF using Gaussian Processescited by 2
  28. 2023Unmatched uncertainty mitigation through neural network supported model predictive controlcited by 2
  29. 2023Learning the References of Online Model Predictive Control for Urban Self-Drivingcited by 2
  30. 2023Projecting basis functions with tensor networks for Gaussian process regressioncited by 2
  31. 2023Reinforcement Learning with Model Predictive Control for Highway Ramp Meteringcited by 2
  32. 2023MPC-Inspired Reinforcement Learning for Verifiable Model-Free Controlcited by 2
  33. 2024Loss Function Considering Dead Zone for Neural Networkscited by 2
  34. 2024Data-Driven Stochastic Optimal Control in Reproducing Kernel Hilbert Spacescited by 2
  35. 2025Generative Machine Learning in Adaptive Control of Dynamic Manufacturing Processes: A Reviewcited by 2
  36. 2025Context-Aware Deep Lagrangian Networks for Model Predictive Controlcited by 2
  37. 2021Combining Gaussian processes and polynomial chaos expansions for stochastic nonlinear model predictive controlcited by 1
  38. 2021Distributed Bayesian Online Learning for Cooperative Manipulationcited by 1

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