Thesis defence by Daniel Martin Xavier

Model Predictive Control (MPC) provides a powerful framework for controlling nonlinear systems under constraints, but its reliance on repeatedly solving optimization problems can make real-time deployment computationally prohibitive. This limitation is particularly critical in engineering applications where decisions must be taken within milliseconds, and computational delays undermine performance and safety. This thesis investigates learning-based control laws as a means to reduce the computational cost of real-time applications. The controller is modeled by a feedforward neural network that maps the current state and reference to a control input. Both supervised and unsupervised training paradigms are considered to approximate the MPC feedback law, thereby shifting the computational burden from solving an optimization problem online to training a neural network offline and evaluating it efficiently in real time. Since data-driven strategies do not automatically enforce constraints, a one-step filter is introduced to promote feasibility by minimally correcting the network’s output. The second aspect of the methodology involves quantifying the approximation error by deriving Rademacher-complexity generalization bounds for supervised neural policies. Additionally, the training error convergence is analyzed for underparameterized networks in the feature-learning regime using the Neural Tangent Kernel formalism. All numerical developments are validated through closed-loop simulations on two illustrative benchmarks (Van der Pol oscillator and four-tank system), as well as two engineering applications: open-die forging and wind turbines. These results outline a data-driven control framework that reduces online computational cost while providing theoretical insights for for future guarantees in real-time applications.

Composition du jury :

• M. Luc JAULIN,  Professeur des Universités, École Nationale Supérieure de Techniques Avancées, Rapporteur
• M. Nazih MECHBAL, Professeur des Universités, École Nationale Supérieure d’Arts et Métiers, Rapporteur
• Mme Sylvie PUTOT, Professeure des Universités, École Polytechnique, Examinatrice
• M. Gael CHEVALLIER, Professeur des Universités, Université of Franche-Comté, Examinateur