Text only print
Full screen print
FJ-LMI Seminar
Seminar information archive ～02/14｜Next seminar｜Future seminars 02/15～
| Organizer(s) | Toshiyuki Kobayashi, Michael Pevzner |
|---|
Next seminar
2026/03/18
13:30-14:15 Room #056 (Graduate School of Math. Sci. Bldg.)
Amaury HAYAT (ENPC, Paris)
Stabilization of PDEs and AI for mathematics (英語)
https://fj-lmi.cnrs.fr/seminars/
Amaury HAYAT (ENPC, Paris)
Stabilization of PDEs and AI for mathematics (英語)
[ Abstract ]
Control theory consists in asking: if we can act on a system, what can we make it do? One of the main problems is the stabilization problem: how can we act on a system to guarantee the long-term behavior of its solutions? In this presentation, we will examine this problem from several angles. First, we will look at the problem of stabilizing PDEs from an abstract perspective and present a recent approach called F-equivalence (or sometimes Fredholm backstepping). The principle is simple: instead of trying to find a control that makes the system stable, we look at another problem: we try find a control that renders the PDE system dynamically equivalent to a simpler system for which stability is already known. Besides being interesting in itself, this approach has also resulted in new results in control theory, and we will review the progress that has been made in the last three years. In a second part, we will focus on a more concrete problem: the stabilization of hyperbolic equations modeling road traffic. We will show how abstract mathematical concepts, such as entropic solutions, can have tangible impacts in real-world scenarios, and we will discuss their application to traffic regulation and the reduction of traffic jams.
[ Reference URL ]Control theory consists in asking: if we can act on a system, what can we make it do? One of the main problems is the stabilization problem: how can we act on a system to guarantee the long-term behavior of its solutions? In this presentation, we will examine this problem from several angles. First, we will look at the problem of stabilizing PDEs from an abstract perspective and present a recent approach called F-equivalence (or sometimes Fredholm backstepping). The principle is simple: instead of trying to find a control that makes the system stable, we look at another problem: we try find a control that renders the PDE system dynamically equivalent to a simpler system for which stability is already known. Besides being interesting in itself, this approach has also resulted in new results in control theory, and we will review the progress that has been made in the last three years. In a second part, we will focus on a more concrete problem: the stabilization of hyperbolic equations modeling road traffic. We will show how abstract mathematical concepts, such as entropic solutions, can have tangible impacts in real-world scenarios, and we will discuss their application to traffic regulation and the reduction of traffic jams.
https://fj-lmi.cnrs.fr/seminars/
