mlsanityData to 14 Oct 2026

Model-Free Predictive Control: Introductory Algebraic Calculations, and a Comparison with HEOL and ANNs

arXiv 2502.00443 ↗First posted 1 Feb 2025eess.SY cs.AI cs.SYcited by 1

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Abstract (arXiv)

Model predictive control (MPC) is a popular control engineering practice, but requires a sound knowledge of the model. Model-free predictive control (MFPC), a burning issue today, also related to reinforcement learning (RL) in AI, is reformulated here via a linear differential equation with constant coefficients, thanks to a new perspective on optimal control combined with recent advances in the field of model-free control (MFC). It is replacing Dynamic Programming, the Hamilton-Jacobi-Bellman equation, and Pontryagin's Maximum Principle. The computing burden is low. The implementation is straightforward. Two nonlinear examples, a chemical reactor and a two tank system, are illustrating our approach. A comparison with the HEOL setting, where some expertise of the process model is needed, shows only a slight superiority of the later. A recent identification of the two tank system via a complex ANN architecture might indicate that a full modeling and the corresponding machine learning mechanism are not always necessary neither in control, nor, more generally, in AI.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 9 of its 61 references that are in the map. First posted on arXiv 1 Feb 2025.

Builds on

9 of 61 references.

References · 9

  1. 2018A Tour of Reinforcement Learning: The View from Continuous Controlcited by 151
  2. 2022Real-time Neural-MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platformscited by 41
  3. 2019Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Controlcited by 17
  4. 2013Model-free controlcited by 7
  5. 2024Model Predictive Control and Reinforcement Learning: A Unified Framework Based on Dynamic Programmingcited by 7
  6. 2025Synchronization of Kuramoto oscillators via HEOL, and a discussion on AIcited by 3
  7. 2021An alternative to proportional-integral and proportional-integral-derivative regulators: Intelligent proportional-derivative regulatorscited by 2
  8. 2024Flatness-based control revisited: The HEOL settingcited by 2
  9. 2024The Euler-Lagrange equation and optimal control: Preliminary resultscited by 2

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Cited by year

Citing papers per year: 2025: 1.

1 paper.

  1. 2025Avoidance of an unexpected obstacle without reinforcement learning: Why not using advanced control-theoretic tools?cited by 0

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  1. 2025Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classification
  2. 2025Computationally efficient Gauss-Newton reinforcement learning for model predictive control
  3. 2024Faster Model Predictive Control via Self-Supervised Initialization Learning
  4. 2026A Systematic Review and Taxonomy of Reinforcement Learning-Model Predictive Control Integration for Linear Systems
  5. 2026Optimal Control with Learned Critics under Unmodeled State Dependencies
  6. 2018Differentiable MPC for End-to-end Planning and Control
  7. 2026Dream-MPC: Gradient-Based Model Predictive Control with Latent Imagination
  8. 2025Intersection of Reinforcement Learning and Bayesian Optimization for Intelligent Control of Industrial Processes: A Safe MPC-based DPG using Multi-Objective BO