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arXiv · 2502.00443

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

Cédric Join·Emmanuel Delaleau·Michel Fliess
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Abstract

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.

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Cédric Join, Emmanuel Delaleau, Michel Fliess. 2025-04-22. Model-Free Predictive Control: Introductory Algebraic Calculations, and a Comparison with HEOL and ANNs. https://arxiv.org/abs/2502.00443

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