Model-Free Predictive Control: Introductory Algebraic Calculations, and a Comparison with HEOL and ANNs
Cédric Join, Emmanuel Delaleau, Michel Fliess
TL;DR
The paper proposes model-free predictive control (MFPC) as a practical, algebraic alternative to MPC, leveraging an ultra-local model $\dot{y} = \mathcal{F} + \alpha u$ and a data-driven estimation of $\mathcal{F}$ to bridge predictive control with reinforcement learning. By deriving an Euler-Lagrange-based optimization under constant $F$, it obtains a simple, second-order dynamics $\ddot{y} - \alpha^2 (y - y_{\text{setpoint}}) = 0$ and demonstrates a horizon-receding optimization on each interval using $\mathcal{F}_{\text{est}}$, while also presenting the HEOL tangent-linear and iP-control framework for comparison. The authors validate MFPC on two nonlinear nonlinearities—an chemical reactor and a two-tank system—and show that MFPC achieves satisfactory performance with minimal modeling effort, often closing the gap with HEOL, and highlighting that full modeling and ANN-based approaches are not always necessary in control or AI contexts. Overall, the work supports a model-free, data-driven control paradigm that reduces modeling requirements, maintains robustness to disturbances, and offers a computationally light alternative to traditional MPC and some RL-based methods.
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.