# Oberseminar "Numerische Mathematik, Optimierung und dynamische Systeme"

Oberseminar , Nummer im Vorlesungsverzeichnis: 10525

SWS: 2

## Allgemeines

gemeinsames Oberseminar der Lehrstühle für Angewandte Mathematik und Ingenieurmathematik

# Vortragsankündigungen für das Oberseminar

Im Rahmen unseres gemeinsamen Oberseminars finden folgende Vorträge statt:

Am Montag, dem 13. Juli 2015, um 16:15 Uhr im S 82, spricht

 Herr Ph.D. Dante Kalise Research Group "Optimization and Optimal Control" (OOC) Johann Radon Institute for Computational and Applied Mathematics (RICAM) Austrian Academy of Sciences in Linz, Österreich

über das Thema

 "Towards optimal feedback control of high-dimensional systems".

## Abstract:

Feedback control design plays a fundamental role in modern engineering. For an optimality-based formulation of the control problem, the Dynamic Programming Principle allows the characterization of the associated value function as the viscosity solution of a first-order, fully nonlinear Hamilton-Jacobi-Bellman equation. The equation is defined over the state-space of the controlled dynamical system and therefore, even control problems over low-dimensional dynamics lead to HJB equations of high complexity. In this talk, we present an approximation framework to compute (sub)optimal feedback controllers based on the solution of a Generalized HJB equation and a policy iteration algorithm. Problems arising from the feedback control of partial differential equations illustrate the effectiveness of our approach in a high-dimensional context.

Am Montag, dem 22. Juni 2015, um 16:15 Uhr im S 82, spricht

 Herr Dipl.-Math. Johannes Michael Ingenieurmathematik Institut für Mathematik und Rechneranwendung (LRT1) Fakultät für Luft- und Raumfahrttechnik (LRT) Universität der Bundeswehr München

über das Thema

 "Optimal Control in vertical vehicle dynamics – About singular event detection and impulsive system dynamics – ".

## Abstract:

Nowadays, cars contain a vast number of sensors to improve safety and comfort of the passengers. With today's small and reliable distance and camera sensors it is not only possible to detect whether there are obstacles in the path, but also to capture the surface of the pavement in front of the car. This information allows for adaptations of chassis characteristics such as the damping coefficients of the chassis dampers. A lot of research has been carried out to use such preview information as additional input in suspension control, like linear quadratic regulators, model predictive control and stochastic models using classical multibody dynamics.
This talk covers the occurrence of singular events like bumps and steps. Two problems are presented that cover different aspects of the optimal control. The first one utilizes the well-known sensitivity theorem of Fiacco to obtain a real-time algorithm for the upcoming road irregularities using an event detection method. The second formulation is about the extension of the classical dynamic models to incorporate contact loss between tyre and road at the transition of the singular events.

Am Montag, dem 15. Juni 2015, um 16:15 Uhr im S 82, spricht

 Herr Dr. Armin Rund Institut fur Mathematik und Wissenschaftliches Rechnen Naturwissenschaftliche Fakultät Karl-Franzens-Universität Graz, Linz, Österreich

über das Thema

 "Switching control based on sparsity".

## Abstract:

A novel formulation for switching controls based on convex analysis techniques related to sparse control is introduced. Using a Moreau-Yosida approximation, a family of approximating problems is introduced that is amenable for efficient numerical realization of switching controls using a semismooth Newton method in function space. Numerical experiments for the heat equation and the competitive Lotka-Volterra equations are included.

Am Montag, dem 18. Mai 2015, um 16:15 Uhr im S 82, spricht

 Herr Dr. Roberto Guglielmi Research Group "Optimization and Optimal Control" (OOC) Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Österreich

über das Thema

 "Null controllability of degenerate parabolic equations".

## Abstract:

After a survey on the current state of the art of the controllability for degenerate parabolic equations, we focus on the study of the controllability properties of a class of generalized Grushin operator of parabolic type, where the degeneracy occurs in the interior of the space domain. We show that the null controllability holds true only for reasonably weak degeneracies, and possibly under a minimum time assumption. Moreover, in connection with the study of the Laplace-Beltrami operator on manifold with almost Riemannian metrics, we analyze the case of a Grushin operator with a inverse square singular potential, and we show partial positive results on the null controllability of this operator.

Am Montag, dem 27. April 2015, um 16:15 Uhr im S 82, spricht

 Herr Dr. Timm Faulwasser Automatic Control Laboratory 1 (LA 1) Institute of Mechanical Engineering (IGM) School of Engineering (STI) École polytechnique fédérale de Lausanne (EPFL), Lausanne, Schweiz

über das Thema

 "On the Design of Predictive Controllers Based on Turnpike Properties".

## Abstract:

In the last two decades nonlinear model predictive control (NMPC) has received a lot of attention by both theoreticians, in the field of systems and control, and practitioners, mainly from process industries.
In this talk, we discuss the design of sampled-data NMPC based on turnpike properties. While often stability of NMPC schemes is enforced by means of terminal constraints and end penalties, we show that turnpike properties enable avoiding such constraints/penalties in different NMPC formulations.
We begin the talk with a formal introduction of turnpike properties of continuous-time optimal control problems (OCP) [1,2]. Turnpike properties describe a property of OCPs, whereby, for varying initial conditions and horizons, the solutions stay close to a specific steady state during the major part of the time horizon. It is worth to be mentioned that turnpike properties have been intensively investigated in the context of optimal control approaches to economic problems [1,3]. However, it is surprising that turnpike properties have received only limited attention in the context of NMPC [4, 5]. In this presentation, we discuss results attempting to partially bridge this gap in a continuous-time setting. We show that exact turnpikes allow establishing finite-time convergence to the optimal steady state and recursive feasibility without any terminal constraints [6]. We also discuss the question of convergence in the case of approximate turnpikes. We draw upon examples from different areas such as process control and biology to illustrate our results.
 [1] D.A. Carlson, A. Haurie, and A. Leizarowitz. (1991). Infinite Horizon Optimal Control: Deterministic and Stochastic Systems. Springer Verlag. [2] T. Faulwasser, M. Korda, C.N. Jones, and D. Bonvin. Turnpike and dissipativity properties in dynamic real-time optimization and economic MPC. Proc. of the 53rd IEEE on Decision and Control (CDC), Los Angeles, California, USA, 2014, p. 2734-2738. [3] L. McKenzie. Turnpike theory. Econometrica: Journal of the Econometric Society, 1976, 44(5), 841–865. [4] M. Ellis, H. Durand, and P. Christofides. A tutorial review of economic model predictive control methods. Journal of Process Control, 2014, 24(8), 1156–1178. [5] L. Grüne. Economic receding horizon control without terminal constraints. Automatica, 2013, 49, 725-734. [6] T. Faulwasser & D. Bonvin. On the design of economic NMPC based on an exact turnpike property. To appear in Proc. 9th International Symposium on Advanced Control of Chemical Processes (ADCHEM), Whistler, Canada, 2015.

Am Montag, dem 20. April 2015, um 16:15 Uhr im S 82, spricht

 Herr Dr. Michael Schönlein Lehrstuhl für Mathematik II Institut für Mathematik Fakultät für Mathematik und Informatik Julius-Maximilians-Universität Würzburg

über das Thema

 "Controllability of Ensembles of Linear Dynamical Systems".

## Abstract:

We investigate the task of controlling ensembles of initial and terminal state vectors of parameter-dependent linear systems by applying parameter-independent open loop controls. From a functional analytic point of view, the problem of ensemble controllability is equivalent to approximate controllability of infinite-dimensional systems defined on Banach or Hilbert spaces. Standard characterizations of approximate controllability in Hilbert spaces are, except for very special cases, not easily applicable for ensemble control. In this talk we present a new function theory approach to uniform ensemble controllability. Using classical approximation theoretic results, such as the Stone-Weierstrass Theorem and Mergelyan's Theorem, we present necessary, as well as sufficient conditions for ensemble controllability. It turns out that, up to a technical condition, the ensemble control problem for continuous-time and discrete-time systems are equivalent. For real analytic families of linear systems it is shown that ensemble controllability holds only for systems with at most two independent parameters. Our approach is based on information of the spectrum of the system matrices. An open problem is to find relaxed necessary and sufficient conditions using the concept of pseudospectra.