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A robust and adaptive MPC formulation for Gaussian process models

arXiv 2507.02098 ↗First posted 2 Jul 2025eess.SY cs.LG cs.SYcited by 0

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Abstract (arXiv)

In this paper, we present a robust and adaptive model predictive control (MPC) framework for uncertain nonlinear systems affected by bounded disturbances and unmodeled nonlinearities. We use Gaussian Processes (GPs) to learn the uncertain dynamics based on noisy measurements, including those collected during system operation. As a key contribution, we derive robust predictions for GP models using contraction metrics, which are incorporated in the MPC formulation. The proposed design guarantees recursive feasibility, robust constraint satisfaction and convergence to a reference state, with high probability. We provide a numerical example of a planar quadrotor subject to difficult-to-model ground effects, which highlights significant improvements achieved through the proposed robust prediction method and through online learning.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 31 of its 69 references that are in the map. First posted on arXiv 2 Jul 2025.

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31 of 69 references.

References · 31

  1. 2018GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Accelerationcited by 609
  2. 2017On Kernelized Multi-armed Banditscited by 352
  3. 2018Learning-based Model Predictive Control for Safe Explorationcited by 120
  4. 2017Cautious Model Predictive Control using Gaussian Process Regressioncited by 91
  5. 2019acados: a modular open-source framework for fast embedded optimal controlcited by 68
  6. 2021Practical and Rigorous Uncertainty Bounds for Gaussian Process Regressioncited by 49
  7. 2021Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overviewcited by 45
  8. 2015Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Designcited by 39
  9. 2021Data-Driven MPC for Quadrotorscited by 35
  10. 2020Deterministic error bounds for kernel-based learning techniques under bounded noisecited by 24
  11. 2024ActSafe: Active Exploration with Safety Constraints for Reinforcement Learningcited by 23
  12. 2019A computationally efficient robust model predictive control framework for uncertain nonlinear systems -- extended versioncited by 14
19 more
  1. 2023Automatic nonlinear MPC approximation with closed-loop guaranteescited by 12
  2. 2022Robust and Kernelized Data-Enabled Predictive Control for Nonlinear Systemscited by 9
  3. 2019Linear robust adaptive model predictive control: Computational complexity and conservatism -- extended versioncited by 8
  4. 2022Robust adaptive MPC using control contraction metricscited by 8
  5. 2024Safe Guaranteed Exploration for Non-linear Systemscited by 8
  6. 2019Robust Adaptive Model Predictive Control: Performance and Parameter Estimationcited by 7
  7. 2019A robust adaptive model predictive control framework for nonlinear uncertain systemscited by 7
  8. 2022State space models vs. multi-step predictors in predictive control: Are state space models complicating safe data-driven designs?cited by 6
  9. 2024Towards safe and tractable Gaussian process-based MPC: Efficient sampling within a sequential quadratic programming frameworkcited by 6
  10. 2025Gaussian processes for dynamics learning in model predictive controlcited by 6
  11. 2020KPC: Learning-Based Model Predictive Control with Deterministic Guaranteescited by 5
  12. 2025Finite-Sample-Based Reachability for Safe Control with Gaussian Process Dynamicscited by 5
  13. 2022Zero-Order Optimization for Gaussian Process-based Model Predictive Controlcited by 4
  14. 2024Towards safe Bayesian optimization with Wiener kernel regressioncited by 4
  15. 2025Stochastic Model Predictive Control for Sub-Gaussian Noisecited by 4
  16. 2025Optimal kernel regression bounds under energy-bounded noisecited by 4
  17. 2021Tube-Certified Trajectory Tracking for Nonlinear Systems With Robust Control Contraction Metricscited by 3
  18. 2024L4acados: Learning-based models for acados, applied to Gaussian process-based predictive controlcited by 2
  19. 2021Robust Adaptive Model Predictive Control of Quadrotorscited by 1

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