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<p><span class="">Değerli Liste Üyeleri, detayları aşağıda verilen
seminere sizleri davet etmek isteriz. İyi çalışmalar,<br>
<br>
kağan</span></p>
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</span></p>
<p><span class=""><br>
</span></p>
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<div class=""><b class="">MATHEMATICS COLLOQUIUM</b></div>
<div class=""><b class=""><br class="">
</b></div>
<div class="">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.</div>
<div class=""><br class="">
</div>
<div class="">
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style="font-family: Arial, sans-serif;">
<hr class="" align="center" size="2" width="100%"></span></div>
<div class="" style="margin: 0cm 0cm 0.0001pt;"><b class="">Türker
Özsarı</b></div>
<div class="" style="margin: 0cm 0cm 0.0001pt;"><br class="">
</div>
<div class="" style="margin: 0cm 0cm 0.0001pt;">Title: <span
style="text-align: center;" class=""><span
style="line-height: 107%;" class="" lang="EN-US">Pseudo-backstepping
and
stabilization of the Korteweg-de-Vries equation</span></span></div>
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<div class="" style="margin: 0cm 0cm 0.0001pt;">Abstract: <span
style="font-family: Tahoma;" class="">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.</span><span style="font-family: Tahoma;" class=""> </span><span
style="font-family: Tahoma;" class="">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.</span><span style="font-family:
Tahoma;" class=""> </span><span style="font-family:
Tahoma;" class="">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.</span><span style="font-family: Tahoma;" class="">
</span><span style="font-family: Tahoma;" class="">Finally,
we give numerical simulations
illustrating the efficacy of our controllers.</span><span
style="font-family: Tahoma;" class=""> </span></div>
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<p class="MsoNormal"><span
style="font-family:Tahoma;mso-fareast-font-family:
"Adobe Kaiti Std R"" class="" lang="EN-US">This
is a joint work with A. Batal (IZTECH) and this
research is funded by IZTECH BAP Grant# 2017IYTE14.<o:p
class=""></o:p></span></p>
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<div class="">
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt;
font-size: 12pt; font-family: "Times New Roman",
serif; text-align: center;" align="center"><span class=""
style="font-family: Arial, sans-serif;">
<hr class="" align="center" size="2" width="100%"></span></div>
<div class="" style="margin: 0cm 0cm 0.0001pt;">Kind regards,</div>
<div class="" style="margin: 0cm 0cm 0.0001pt;"><br class="">
</div>
<div class="" style="margin: 0cm 0cm 0.0001pt;">Yasemin <br>
<br>
<br>
<br>
<pre class="moz-signature" cols="72">p.s. Sabancı Üniv kampüsüne ulaşım için <a class="moz-txt-link-freetext" href="http://www.sabanciuniv.edu/tr/ulasim/ring-sefer-saatleri">http://www.sabanciuniv.edu/tr/ulasim/ring-sefer-saatleri</a> adresine bakınız.
</pre>
</div>
<div class="" style="margin: 0cm 0cm 0.0001pt;"><br class="">
</div>
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