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Chair of Applied Mathematics
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(MATHE V)
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Oberseminar in WS 2007/08
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Vortragsankündigungen für das Oberseminar
Im Rahmen unseres gemeinsamen Oberseminars
finden folgende Vorträge
statt:
Am
Montag, dem 04. Februar 2008, um 16.00 Uhr c.t. im
S 82, Gebäude NW II, spricht
über das Thema
| "Functional Type Error Majorants for Optimal Control Problems".
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Einladung (PDF-file)
Abstract:
We present an approach to the a posteriori analysis of a class of optimal
control problems governed by elliptic partial differential equations
with constraints in the control. It is based on functional type a posteriori
estimates that provide sharp bounds for the error with respect
to any feasible approximation of the state. They allow to derive computable
two-sided a posteriori estimates for the cost functional and give rise
to a posteriori estimates of errors in the control and the state,
measured in a combined norm.
Am
Montag, dem 10. Dezember 2007, um 16.00 Uhr c.t. im
S 82, Gebäude NW II, spricht
über das Thema
| "Poiseuille und Quetschströmungen zwischen
gewellten Platten".
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Einladung (PDF-file)
Am
Dienstag, dem 04. Dezember 2007, um 13.00 Uhr c.t. im
H 20, Gebäude NW II, spricht
über das Thema
| "Global Optimization of Discrete Topology
Design Problems".
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Einladung (PDF-file)
Abstract:
A classical problem within the field of structural topology optimization
is to find the stiffest structure subject to multiple loads and a bound on
the volume (or weight) of the structure. We minimize a weighted average of
the compliances, i.e. the inverse of the stiffness. The design variables
describe the cross sectional areas of the bars in a truss or fiber
directions in laminated composite structure. This class of optimal design
problems is well-studied for continuous design variables. We consider the
situation that the variables are discrete.
Our goal is to compute guaranteed globally optimal structures. We present
a method for the computation of a global optimizer of the underlying
non-convex mixed discrete problem. The method is a finitely convergent
nonlinear branch and cut method tailored to solve large-scale instances of
the original discrete problem. The branch and cut algorithm is based on
solving a sequence of continuous relaxations, which are obtained by
relaxing the discreteness requirements. The main effect of this approach
lies in the fact that these relaxed problems can be equivalently
reformulated as all-quadratic convex problems and thus can be efficiently
solved to global optimality.
The presented nonlinear branch and cut method is numerically compared to a
commercial branch and cut method applied to convex mixed 0-1 equivalent
reformulations of the original discrete problem. The commercial software
solves significantly more relaxations. The main reason for this behavior
is explained by comparing the strength of the relaxations used. We present
global optimal solutions to several large-scale numerical examples.
Am
Montag, dem 22. Oktober 2007, um 16.00 Uhr c.t. im
S 82, Gebäude NW II, spricht
über das Thema
| "Stabilitätsanalyse und Entwurf nichtlinearer
prädiktiver Regelungsverfahren
ohne Endbeschränkungen".
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Zusammenfassung (PDF-file):
Die Prädiktive Regelung (im Englischen “model predictive control” oder
“receding horizon control”) ist eine weit verbreitete Methode zur
online-optimierungsbasierten Regelung komplexer Systeme. Obwohl seit den
1970er Jahren industriell genutzt, wurden wichtige Aspekte
dieses Verfahrens – insbesondere im nichtlinearen Fall –
erst in den letzten Jahren mathematisch verstanden.
In diesem Vortrag wird zunächst eine ausführliche Einführung
in die prädiktive Regelung gegeben und dann eine neue Methode zur
Analyse von Effizienz und Stabilität dieser Verfahren vorgestellt.
Darauf aufbauend wird schließlich an Beispielen erläutert,
wie man das online zu lösende Optimalsteuerungsproblem formulieren
kann, so dass dieses einfach (und damit schnell) zu lösen ist
und gleichzeitig zu einer effizienten und zuverlässigen Regelung
führt.
Am
Donnerstag, dem 04. Oktober 2007, um 10.00 Uhr s.t. im
S 84, Gebäude NW II, spricht
über das Thema
| "The One-Sided Lipschitz Condition in
Differential Inclusions".
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Abstract (PDF-file):
Differential inclusions (differential equations with sets replacing the
right-hand sides) appear naturally in the control theory and in differential
equations with discontinuous or uncertain right-hand sides.
The classical theory of ODEs and estimates for discrete approximations
usually require Lipschitz continuity of the right-hand side in the state
variable. The weaker one-sided Lipschitz (OSL) condition is known for a
long time in the theory of stiff ODE. Proper extensions of this condition
to set-valued functions appeared in 1990.
The OSL condition we consider generalizes the classical Lipschitz condition
and notions of dissipative/ monotone single-valued and set-valued functions.
In the generalized Filippov theorem (1998), the exponential Lipschitz
stability of the trajectories set was established for inclusions
with OSL right-hand sides.
If the OSL constant is negative, the system is strongly (set-valued)
dissipative.
We survey various results following from this theorem:
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– error estimates of the Euler method for (discontinuous)
OSL right-hand sides;
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– exponential formula for the reachable sets;
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– existence of a strongly invariant attractor approximated
by set-iterations for negative OSL constant, etc.
Finally, some open problems are discussed.
Einladende:
©
Klothilde Dulleck
(![[email-Adresse von Klothilde Dulleck]](http://www.mathematik.uni-bayreuth.de/~mathe5/pictures/email_dulleck.gif)
),
WWW-Administrator vom Lehrstuhl Mathematik V
(![[email-Adresse vom WWW-Administrator]](http://www.mathematik.uni-bayreuth.de/~mathe5/pictures/email_www5.gif)
)
Last modified: $Date: 2011/04/27 19:27:11 $
Chair of Appl. Math.