mlsanityData to 14 Oct 2026

Differentiable Nonlinear Model Predictive Control

arXiv 2505.01353 ↗First posted 2 May 2025math.OC cs.AI cs.LGcited by 6

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Abstract (arXiv)

The efficient computation of parametric solution sensitivities is a key challenge in the integration of learning-enhanced methods with nonlinear model predictive control (MPC), as their availability is crucial for many learning algorithms. This paper discusses the computation of solution sensitivities of general nonlinear programs (NLPs) using the implicit function theorem (IFT) and smoothed optimality conditions treated in interior-point methods (IPM). We detail sensitivity computation within a sequential quadratic programming (SQP) method which employs an IPM for the quadratic subproblems. Previous works presented in the machine learning community are limited to convex or unconstrained formulations, or lack an implementation for efficient sensitivity evaluation. The publication is accompanied by an efficient open-source implementation within the acados framework, providing both forward and adjoint sensitivities for general optimal control problems, achieving speedups exceeding 3x over the state-of-the-art solvers mpc.pytorch and cvxpygen.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 32 of its 90 references that are in the map. First posted on arXiv 2 May 2025.

Builds on

32 of 90 references.

References · 32

  1. 2017OptNet: Differentiable Optimization as a Layer in Neural Networkscited by 599
  2. 2019Differentiable Convex Optimization Layerscited by 465
  3. 2019Meta-Learning with Differentiable Convex Optimizationcited by 461
  4. 2018Differentiable MPC for End-to-end Planning and Controlcited by 189
  5. 2017OSQP: An Operator Splitting Solver for Quadratic Programscited by 161
  6. 2018Stochastic subgradient method converges on tame functionscited by 124
  7. 2020Interior Point Solving for LP-based prediction+optimisationcited by 83
  8. 2019Data-driven Economic NMPC using Reinforcement Learningcited by 68
  9. 2019acados: a modular open-source framework for fast embedded optimal controlcited by 68
  10. 2022Theseus: A Library for Differentiable Nonlinear Optimizationcited by 65
  11. 2019Pontryagin Differentiable Programming: An End-to-End Learning and Control Frameworkcited by 52
  12. 2024Clarabel: An interior-point solver for conic programs with quadratic objectivescited by 44
20 more
  1. 2021Nonsmooth Implicit Differentiation for Machine Learning and Optimizationcited by 43
  2. 2025Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classificationcited by 26
  3. 2020HPIPM: a high-performance quadratic programming framework for model predictive controlcited by 23
  4. 2020Learning for MPC with Stability & Safety Guaranteescited by 14
  5. 2024Reinforcement Learning-based Model Predictive Control for Greenhouse Climate Controlcited by 10
  6. 2021MPC-based Reinforcement Learning for Economic Problems with Application to Battery Storagecited by 8
  7. 2024AC4MPC: Actor-Critic Reinforcement Learning for Nonlinear Model Predictive Controlcited by 6
  8. 2023FATROP : A Fast Constrained Optimal Control Problem Solver for Robot Trajectory Optimization and Controlcited by 5
  9. 2023Imitation Learning from Nonlinear MPC via the Exact Q-Loss and its Gauss-Newton Approximationcited by 5
  10. 2021A Dual Active-Set Solver for Embedded Quadratic Programming Using Recursive LDL' Updatescited by 4
  11. 2022Fast integrators with sensitivity propagation for use in CasADicited by 4
  12. 2022Embedded Code Generation with CVXPYcited by 3
  13. 2022Equivalence of Optimality Criteria for Markov Decision Process and Model Predictive Controlcited by 3
  14. 2023BP-MPC: Optimizing the Closed-Loop Performance of MPC using BackPropagationcited by 3
  15. 2025Code generation for solving and differentiating through convex optimization problemscited by 3
  16. 2014Controlling the level of sparsity in MPCcited by 2
  17. 2025MPC4RL -- A Software Package for Reinforcement Learning based on Model Predictive Controlcited by 2
  18. 2023Gauss-Newton Runge-Kutta Integration for Efficient Discretization of Optimal Control Problems with Long Horizons and Least-Squares Costscited by 1
  19. 2024Advanced-Step Real-time Iterations with Four Levels -- New Error Bounds and Fast Implementation in acadoscited by 1
  20. 2024Multi-Phase Optimal Control Problems for Efficient Nonlinear Model Predictive Control with acadoscited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 4.

6 papers.

  1. 2025Differentiable Model Predictive Control on the GPUcited by 7
  2. 2025Safe Reinforcement Learning using Action Projection: Safeguard the Policy or the Environment?cited by 5
  3. 2026TurboMPC: Fast, Scalable, and Differentiable Model Predictive Control on the GPUcited by 2
  4. 2026Accelerating Reinforcement Learning via MPC Solver-Gradient Guidance for Weights-varying MPCcited by 0
  5. 2026lapanda: A Matrix-Free Differentiable Solver for Nonconvex Constrained Optimization Layerscited by 0
  6. 2026Scalable Identification of Physics-Based and Neural Dynamics from Partial Measurementscited by 0