Titre : Rapid stabilization of PDEs with disturbances.
Résumé : In this talk, we analyze the rapid stabilization of two classes of partial differential equations affected by unknown localized disturbances. We first consider an unstable wave equation with a boundary disturbance, where a feedback law acting at the same point as the perturbation guarantees exponential decay of the energy for any prescribed rate. Then, we study a parabolic model with an interior disturbance and design a localized feedback based on spectral inequalities and Lyapunov techniques. In both cases, the inclusion of the multivalued sign operator provides robustness with respect to the unknown disturbance. The well-posedness of the closed-loop system is established using the theory of maximal monotone operators. This talk is based on joint works with A. Huerta, P. Guzmán, and C. Calle.
Bio : Hugo Parada Ríos is a postdoctoral researcher in Mathematics at Inria Nancy, within the SPHINX team, affiliated with the Institut Élie Cartan de Lorraine, working with A. Duca and R. Buffe. He previously held a postdoctoral position at the Institut de Mathématiques de Toulouse, supervised by F. Boyer.
He completed his Ph.D. in Mathematics at the Laboratoire Jean Kuntzmann (Université Grenoble Alpes) under the supervision of E. Crépeau and C. Prieur, and obtained his M.Sc. in Mathematics at the Universidad Técnica Federico Santa María (Chile), supervised by E. Cerpa and P. Guzmán. His research interests include the stability and controllability properties of coupled PDEs with a focus on network structures, the stabilization of systems under constraints such as saturation, delays, or perturbations, and, more recently, the development of numerical methods for kinetic and plasma physics models.
Lien teams :
https://teams.microsoft.com/l/meetup-join/19%3ameeting_OTlmMzQ5ODAtNWRlNC00M2Y5LWIyMTUtMmIzNjg2Nzc5MTk0%40thread.v2/0?context=%7b%22Tid%22%3a%22158716cf-46b9-48ca-8c49-c7bb67e575f3%22%2c%22Oid%22%3a%223521be73-3051-4026-9abf-02849ed2bae6%22%7d
Numéro de réunion : 386 743 374 423 0
Code secret : T92FF9Vm