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

arXiv: https://arxiv.org/abs/2502.00443 · HTML: https://mlsanity.com/paper/2502.00443/

## Key facts

- Cited by 1 papers 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 (most cited first, 9 of 9)

- [A Tour of Reinforcement Learning: The View from Continuous Control](https://mlsanity.com/paper/1806.09460/) (2018)
- [Real-time Neural-MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms](https://mlsanity.com/paper/2203.07747/) (2022)
- [Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control](https://mlsanity.com/paper/1912.10360/) (2019)
- [Model-free control](https://mlsanity.com/paper/1305.7085/) (2013)
- [Model Predictive Control and Reinforcement Learning: A Unified Framework Based on Dynamic Programming](https://mlsanity.com/paper/2406.00592/) (2024)
- [Synchronization of Kuramoto oscillators via HEOL, and a discussion on AI](https://mlsanity.com/paper/2501.07948/) (2025)
- [An alternative to proportional-integral and proportional-integral-derivative regulators: Intelligent proportional-derivative regulators](https://mlsanity.com/paper/2106.12210/) (2021)
- [Flatness-based control revisited: The HEOL setting](https://mlsanity.com/paper/2408.11580/) (2024)
- [The Euler-Lagrange equation and optimal control: Preliminary results](https://mlsanity.com/paper/2410.07040/) (2024)

## Built on by (most cited first, 1 of 1)

- [Avoidance of an unexpected obstacle without reinforcement learning: Why not using advanced control-theoretic tools?](https://mlsanity.com/paper/2509.03721/) (2025)

## 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.