Date/heure
11 octobre 2022
10:45 - 11:45
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Amaury Hayat
Catégorie d'évènement Séminaire Équations aux Derivées Partielles et Applications (Nancy)
Résumé
As part of control theory, stabilization consists in finding a way to make stable a trajectory of a system on which one has some means of action. In this talk, we will discuss recent advances in stabilization of PDEs, starting with one of the most natural approaches for nonlinear systems, quadratic Lyapunov functions, to more complex approaches such as Fredholm backstepping. Backstepping consists in finding a control operator such that the PDE system can be invertibly mapped to a simpler PDE system for which stability is known. Surprisingly powerful, this approach offers the possibility to deal with very general classes of systems. We will review the origin of the method and present new results that resolve a question opened in 2017 and illustrate it on the rapid stabilization of the linearized water-wave equations. Finally, if time allows we will talk about a completely different subject: teaching mathematics to an AI and we will consider two questions, can we train an AI to predict the solution of a mathematical problem? can we train an AI to prove a statement?