[Turkmath:2975] Sabancı Univ. Mathematics Colloquium - 3 May, Thursday, 1.40 pm.

[Kağan Kurşungöz]

Değerli Liste Üyeleri, detayları aşağıda verilen seminere sizleri davet 
etmek isteriz.  İyi çalışmalar,

kağan




*MATHEMATICS COLLOQUIUM*
*
*
You are cordially invited to attend the colloquium given by Türker 
Özsarı (İzmir Institute of Technology) on Thursday, 3 May 2018, in 
FENS-L055 at 1.40 pm.

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*Türker Özsarı*

Title: Pseudo-backstepping and stabilization of the Korteweg-de-Vries 
equation

Abstract: In this talk, we propose a solution to a well-known open 
problem in control theory related with the backstepping boundary 
stabilization of the Korteweg-de Vries (KdV) equation on a finite 
domain.A backstepping controller is obtained from an integral 
transformation involving a specially constructed kernel. However, this 
method fails as the order of the PDE gets higher or the location of 
controller is changed, and there are serious mathematical challenges in 
finding the right kernel. The purpose of this talk is to introduce 
"pseudo-backstepping," a technique using only an imperfect kernel, which 
is obtained by relaxing some of the conditions enforced in the standard 
backstepping method. We prove that the boundary controllers constructed 
via these imferfect kernels still exponentially stabilize the system 
with the cost of a slower rate of decay.Secondly, we design an observer 
for the KdV equation when there is no access to the medium. We only 
assume that there is a sensor at the left end point of the domain 
capable of measuring the first and second order boundary traces of the 
solution. Using only this partial information available, we construct 
Dirichlet-Neumann boundary controllers for the original system acting at 
the right endpoint so that the system becomes exponentially 
stable.Finally, we give numerical simulations illustrating the efficacy 
of our controllers.

This is a joint work with A. Batal (IZTECH) and this research is funded 
by IZTECH BAP Grant# 2017IYTE14.

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Kind regards,

Yasemin



p.s. Sabancı Üniv kampüsüne ulaşım içinhttp://www.sabanciuniv.edu/tr/ulasim/ring-sefer-saatleri  adresine bakınız.

  


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