Oberseminar "Numerische Mathematik, Optimierung und dynamische Systeme"

Oberseminar , Nummer im Vorlesungsverzeichnis: 10525

SWS: 2

Dozenten

Mario Bebendorf, Kurt Chudej, Lars Grüne, Anton Schiela

Allgemeines

gemeinsames Oberseminar der Lehrstühle für Angewandte Mathematik und Wissenschaftliches Rechnen

Vortragsankündigungen für das Oberseminar

Im Rahmen unseres gemeinsamen Oberseminars finden folgende Vorträge statt:


Am Montag, dem 27. Januar 2020, um 16:15 Uhr im S 82, Gebäude NW II, spricht
Herr Dr. Jukka-Pekka Humaloja
Computing Sciences Unit (see "Research")
Tampere University, Tampere, Finnland

über das Thema
"Controller Design for Boundary Control Systems"

Abstract:

Boundary control systems (BCS) are PDEs where control and observation occur via the boundaries of the spatial domain. This talk considers various control problems for this class of systems and presents control strategies to solve them: the robust output regulation problem (RORP) is solved using an error- feedback controller based on the internal model principle, model predictive control (MPC) is considered in the discrete time setting utilizing Cayley-Tustin time discretization, and an unknown input observer is constructed based on the active disturbance rejection control (ADRC) strategy.

Am Montag, dem 13. Januar 2020, um 16:15 Uhr im S 82, Gebäude NW II, spricht
Herr Dr. Johannes Pfefferer
Lehr- und Forschungseinheit für Optimalsteuerung M17
Fakultät für Mathematik
Technische Universität München

über das Thema
"hp-Finite Elements for Fractional Diffusion"

Abstract:

In this talk we introduce and analyze a numerical scheme based on hp-finite elements to solve boundary value problems involving the spectral fractional Laplacian. The approach is based on a reformulation of the problem posed on a semi-infinite cylinder in one more spatial dimension. After a suitable truncation of this cylinder, the resulting problem is discretized with linear finite elements in the original domain and with hp-finite elements in the extended direction. The proposed approach yields a reduction of the computational complexity in terms of degrees of freedom and even has slightly improved convergence properties compared to the state-of-the-art discretization using linear finite elements for both the original domain and the extended direction. The performance of the method is illustrated by numerical experiments.

Am Montag, dem 16. Dezember 2018, um 16:15 Uhr im S 82, Gebäude NW II, spricht
Herr Dr. Philipp Braun
und School of Electrical Engineering and Computing,
Faculty of Engineering and Built Environment,
University of Newcastle in Newcastle, Australien

über das Thema
"Robust stabilizing controllers with avoidance properties for linear systems with nontrivial drift"

Abstract:

For linear and nonlinear dynamical systems, control problems such as feedback stabilization of target sets and feedback laws guaranteeing obstacle avoidance are topics of interest throughout the control literature. While the isolated problems (i.e., guaranteeing only stability or avoidance) are well understood, the combined control problem guaranteeing stability and avoidance simultaneously is leading to significant challenges even in the case of linear systems. In this talk we highlight difficulties in the controller design with conflicting objectives in terms of guaranteed avoidance of bounded sets and asymptotic stability of the origin. In addition, using the framework of hybrid systems, we propose a partial solution to the combined control problem for underactuated linear systems with nontrivial drift.

Am Montag, dem 9. Dezember 2019, um 16:15 Uhr im S 82, Gebäude NW II, spricht
Herr Doc. Ing. Jiří Outrata, Dr Sc.
Institut für Informationstheorie und Automatisierung (UTIA)
Tschechische Akademie der Wissenschaften (ASCR)
Prag,Tschechische Republik

über das Thema

"On the semismooth* Newton method and its application to a class of Nash equilibria".

Abstract:

On the basis of the concept of semismothness* a new Newton-type method is derived which is applicable to the numerical solution of generalized equations (GEs). If the right-hand side of the considered GE is strongly metrically regular around the solution, then the Newton step may easily be. performed on the basis of the limiting coderivative of the considered multifunction. This method is applied to a GE which governs Nash equilibria in presence of nonsmooth terms in the objectives of the single players.This is a joint research with H. Gfrerer (Linz).

Am Freitag, dem 6. Dezember 2019, um 10:00 Uhr im S 72, Gebäude NW II, spricht
Herr Prof. Dr. Peter Kloeden
Fachbereich Mathematik
Mathematisch-Naturwissenschaftliche Fakultät
Eberhard Karls Universität Tübingen
(Gast am Lehrstuhl für Angewandte Mathematik, Prof. Dr. Lars Grüne)

über das Thema

"Forward attractors and limit sets of nonautonomous difference equations".

Abstract:

The theory of nonautonomous dynamical systems has undergone major development during the past 20 years. Two types of attractors consisting of invariant families of sets have been defined for nonautonomous difference equations, one using pullback convergence with information about the system in the past and the other using forward convergence with information about the system in the future. In both cases, the component sets are constructed using a pullback argument within a positively invariant family of sets. The forward attractor so constructed also uses information about the past, which is very restrictive and not essential for determining future behaviour.
The forward asymptotic behaviour can also be described through the omega-limit set of the system. This set is closely related to what Vishik called the uniform attractor although it need not be invariant. Provided a future uniformity condition holds, it is shown to be asymptotically positively invariant. Hence this omega-limit set provides useful information about the behaviour in current time during the approach to the future limit.

Am Montag, dem 18. November 2019, um 16:15 Uhr im S 82, Gebäude NW II, spricht
Herr Prof. Dr. Vladimir Gaitsgory
Department of Mathematic
Faculty of Science and Engineering
Macquarie University, Sydney, Australien
(Gast am Lehrstuhl für Angewandte Mathematik, Prof. Dr. Lars Grüne)

über das Thema

"Linear Programming Approach to Long Run Average Optimal Control: The Non-Ergodic Case".

Abstract:

We will discuss an infinite dimensional linear programming (IDLP) problem, which along with its dual allow one to characterize the limit optimal values of the infinite time horizon optimal control (OC) problem with time discounting and time averaging criteria. One of the results that we will concentrate on is that establishing that the Abel and Cesaro limits of the optimal value of the OC problem are bounded from above by the optimal value of the IDLP problem and from below by the optimal value of its dual, this implying, in particular, that the Abel and Cesaro limits exist and are equal if there is no duality gap. We will also discuss IDLP based sufficient and necessary optimality conditions for the long-run-average optimal control problem applicable when there is no duality gap. The novelty of our consideration is that it is focused on the general case, when the limit optimal values may depend on initial conditions of the system. The talk is based on results obtained in collaboration with V. Borkar and I. Shvartsman.

Am Dienstag, dem 12. November 2019, um 14:15 Uhr im S 72, Gebäude NW II, spricht
Herr M. Sc. Patrick Jaap
Professur für Numerik partieller Differentialgleichungen
Institut für Numerische Mathematik
Fakultät Mathematik
Technische Universität Dresden

über das Thema
"Discrete Finite Strain Plasticity and its Implementation Challenges".

Abstract:

In this talk a discrete minimization problem is presented which arises from the abstract time-increment finite strain plasticity theory. To attack the problem computationally, an explicit expression of "von Mises" dissipation will be derived. The discrete solution demands a FE space with deformation values in the manifold SL(d) which causes a lot of implementation difficulties compared to linearized small strain plasticity. In the end, the proximal Newton method is presented in hope to be a good solver to obtain the minimizer.
Der Vortrag wird ergänzt durch eine Präsentation von
Herr M. Sc. Bastian Pötzl
Lehrstuhl für Angewandte Mathematik
Mathematisches Institut
Fakultät für Mathematik, Physik und Informatik
Universität Bayreuth
zum Thema
"Introduction to Energetic Formulations of Finite Strain Elastoplasticity".

Am Montag, dem 28. Oktober 2019, um 16:15 Uhr im S 82, Gebäude NW II, spricht
Herr Dr.-Ing. Pavel Osinenko
Professur Regelungstechnik und Systemdynamik
Institut für Automatisierung
Fakultät für Elektrotechnik und Informationstechnik
Technische Universität Chemnitz

über das Thema
"On computational aspects of practical stabilization"

Abstract:

Stabilization of a general nonlinear system can only in exceptional situations be done via classical continuous control methods. The standard scenario is when nonsmooth/discontinuous CLFs and controls need to be employed. The corresponding system analyses are quite elaborate. The most intuitive way to analyze a system under a discontinuous feedback controller is via the sample-and-hold concept, which in turn gives insight into the digital realization. The crucial aspect of sample-and-hold analysis is the choice of appropriate sampling periods. Actual numerical implementations of sample- and-hold analyses are rather scarce. In this talk, we review some of the computational bottlenecks thereof. An example of a verified computation of a sampling time for sample-and-hold sliding-mode control of traction dynamics is provided. The resulting computations turned out to be practicable. There are still open questions that, in our view, require attention.

Einladende:

Prof. Dr. Mario Bebendorf
Prof. Dr. Kurt Chudej
Prof. Dr. Lars Grüne
Prof. Dr. Anton Schiela

Lehrstuhl -

|  Universität Bayreuth -