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

• URL: http://arxiv.org/abs/2502.00443v1
• Date: Sat, 01 Feb 2025 14:23:34 GMT
• Title: Model-Free Predictive Control: Introductory Algebraic Calculations, and a Comparison with HEOL and ANNs
• Authors: Cédric Join, Emmanuel Delaleau, Michel Fliess,
• Abstract summary: Model-free predictive control is reformulated here via a linear differential equation with constant coefficients. It is replacing Dynamic Programming, the Hamilton-Jacobi-Bellman equation, and Pontryagin's Maximum Principle. 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.
• Score: 0.1474723404975345
• License:
• 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. 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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