mlsanityData to 7 Oct 2026

Mapping back and forth between model predictive control and neural networks

arXiv 2404.12030 ↗First posted 18 Apr 2024eess.SY cs.AI cs.SYcited by 1

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Abstract (arXiv)

Model predictive control (MPC) for linear systems with quadratic costs and linear constraints is shown to admit an exact representation as an implicit neural network. A method to "unravel" the implicit neural network of MPC into an explicit one is also introduced. As well as building links between model-based and data-driven control, these results emphasize the capability of implicit neural networks for representing solutions of optimisation problems, as such problems are themselves implicitly defined functions.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 18 of its 30 references that are in the map. First posted on arXiv 18 Apr 2024.

Builds on

18 of 30 references.

References · 18

  1. 2019Deep Equilibrium Modelscited by 603
  2. 2019Implicit Deep Learningcited by 124
  3. 2018Efficient representation and approximation of model predictive control laws via deep learningcited by 55
  4. 2018Learning an Approximate Model Predictive Controller with Guaranteescited by 54
  5. 2021Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustnesscited by 43
  6. 2019Large Scale Model Predictive Control with Neural Networks and Primal Active Setscited by 28
  7. 2022Learning Model Predictive Controllers with Real-Time Attention for Real-World Navigationcited by 27
  8. 2019Near-Optimal Rapid MPC using Neural Networks: A Primal-Dual Policy Learning Frameworkcited by 16
  9. 2021Reliably-stabilizing piecewise-affine neural network controllerscited by 13
  10. 2022Stability Verification of Neural Network Controllers using Mixed-Integer Programmingcited by 10
  11. 2019AReN: Assured ReLU NN Architecture for Model Predictive Control of LTI Systemscited by 9
  12. 2022Model Predictive Control via On-Policy Imitation Learningcited by 6
6 more
  1. 2018Convex searches for discrete-time Zames-Falb multiplierscited by 4
  2. 2022Bounding the difference between model predictive control and neural networkscited by 4
  3. 2020In Proximity of ReLU DNN, PWA Function, and Explicit MPCcited by 2
  4. 2021Tailored neural networks for learning optimal value functions in MPCcited by 2
  5. 2019On the Optimal Control of Relaxation Systemscited by 1
  6. 2022Tailored max-out networks for learning convex PWQ functionscited by 1

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Citing papers per year: 2024: 1.

1 paper.

  1. 2024Convex neural network synthesis for robustness in the 1-normcited by 0