mlsanityData to 7 Oct 2026

Learning an Approximate Model Predictive Controller with Guarantees

arXiv 1806.04167 ↗First posted 11 Jun 2018eess.SY cs.LG cs.SYcited by 54

Not on the map. Why?

Abstract (arXiv)

A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of nonlinear systems. Any standard supervised learning technique (e.g. neural networks) can be employed to approximate the MPC from samples. In order to obtain closed-loop guarantees for the learned MPC, a robust MPC design is combined with statistical learning bounds. The MPC design ensures robustness to inaccurate inputs within given bounds, and Hoeffding's Inequality is used to validate that the learned MPC satisfies these bounds with high confidence. The result is a closed-loop statistical guarantee on stability and constraint satisfaction for the learned MPC. The proposed learning-based MPC framework is illustrated on a nonlinear benchmark problem, for which we learn a neural network controller with guarantees.

Key facts. Cited by 54 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Jun 2018.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2020: 1; 2021: 9; 2022: 8; 2023: 7; 2024: 7; 2025: 12; 2026: 10.

54 papers.

Sort:

By area:

  1. 2021On the Sample Complexity of Stability Constrained Imitation Learningcited by 38
  2. 2021Physics-Informed Neural Nets for Control of Dynamical Systemscited by 31
  3. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  4. 2021Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulatorscited by 21
  5. 2022TaSIL: Taylor Series Imitation Learningcited by 21
  6. 2025Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classificationcited by 19
  7. 2021On Recurrent Neural Networks for learning-based control: recent results and ideas for future developmentscited by 14
  8. 2021Reliably-stabilizing piecewise-affine neural network controllerscited by 13
  9. 2020Synthesizing Decentralized Controllers with Graph Neural Networks and Imitation Learningcited by 12
  10. 2023Automatic nonlinear MPC approximation with closed-loop guaranteescited by 12
  11. 2021Deep Learning Explicit Differentiable Predictive Control Laws for Buildingscited by 11
  12. 2022Stability Verification of Neural Network Controllers using Mixed-Integer Programmingcited by 10
38 more
  1. 2022End-to-End Imitation Learning with Safety Guarantees using Control Barrier Functionscited by 10
  2. 2023Approximate non-linear model predictive control with safety-augmented neural networkscited by 9
  3. 2022Neural Lyapunov Differentiable Predictive Controlcited by 6
  4. 2022Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approachcited by 6
  5. 2022Model Predictive Control via On-Policy Imitation Learningcited by 6
  6. 2024Parameter-Adaptive Approximate MPC: Tuning Neural-Network Controllers without Retrainingcited by 6
  7. 2021STL Robustness Risk over Discrete-Time Stochastic Processescited by 4
  8. 2022Learning Stochastic Parametric Differentiable Predictive Control Policiescited by 4
  9. 2023Imitation Learning from Nonlinear MPC via the Exact Q-Loss and its Gauss-Newton Approximationcited by 4
  10. 2025Tiny Recursive Control: Iterative Reasoning for Efficient Optimal Controlcited by 4
  11. 2022Gesture2Path: Imitation Learning for Gesture-aware Navigationcited by 3
  12. 2023An Improved Data Augmentation Scheme for Model Predictive Control Policy Approximationcited by 3
  13. 2024Self-Supervised Learning of Iterative Solvers for Constrained Optimizationcited by 3
  14. 2025Imitation Learning of MPC with Neural Networks: Error Guarantees and Sparsificationcited by 3
  15. 2025End-to-End Training of High-Dimensional Optimal Control with Implicit Hamiltonians via Jacobian-Free Backpropagationcited by 3
  16. 2023Neural Abstraction-Based Controller Synthesis and Deploymentcited by 2
  17. 2024Combining Federated Learning and Control: A Surveycited by 2
  18. 2025YANNs: Y-wise Affine Neural Networks for Exact and Efficient Representations of Piecewise Linear Functionscited by 2
  19. 2025Zero-Shot Transferable Solution Method for Parametric Optimal Control Problemscited by 2
  20. 2025Data-driven Acceleration of MPC with Guaranteescited by 2
  21. 2025Model-Based Diffusion Sampling for Predictive Control in Offline Decision Makingcited by 2
  22. 2023Formally-Sharp DAgger for MCTS: Lower-Latency Monte Carlo Tree Search using Data Aggregation with Formal Methodscited by 1
  23. 2024On Building Myopic MPC Policies using Supervised Learningcited by 1
  24. 2024Mapping back and forth between model predictive control and neural networkscited by 1
  25. 2025Approximate Model Predictive Control for Microgrid Energy Management via Imitation Learningcited by 1
  26. 2025Distributionally Robust Imitation Learning: Layered Control Architecture for Certifiable Autonomycited by 1
  27. 2026On the Convergence of Jacobian-Free Backpropagation for Optimal Control Problems with Implicit Hamiltonianscited by 1
  28. 2026Neural Operators for Multi-Task Control and Adaptationcited by 1
  29. 2021Generalized Reinforcement Learning for Building Control using Behavioral Cloningcited by 0
  30. 2021Neural Predictive Control for the Optimization of Smart Grid Flexibility Schedulescited by 0
  31. 2024Safe and High-Performance Learning of Model Predicitve Control using Kernel-Based Interpolationcited by 0
  32. 2024Receding Hamiltonian-Informed Optimal Neural Control and State Estimation for Closed-Loop Dynamical Systemscited by 0
  33. 2025Feedback-MPPI: Fast Sampling-Based MPC via Rollout Differentiation -- Adios low-level controllerscited by 0
  34. 2025Zero-Shot Function Encoder-Based Differentiable Predictive Controlcited by 0
  35. 2026ReLU Networks for Model Predictive Control: Network Complexity and Performance Guaranteescited by 0
  36. 2026Towards Safe Learning-Based Non-Linear Model Predictive Control through Recurrent Neural Network Modelingcited by 0
  37. 2026Dynamic Controlled Variables Based Dynamic Self-Optimizing Controlcited by 0
  38. 2026Memory-Computation Tradeoffs in Semi Amortized Parametric Optimizationcited by 0

50 most cited of 54 All 54 (JSON)