Oberseminar "Numerische Mathematik, Optimierung und dynamische Systeme"
Nummer im Vorlesungsverzeichnis: 10525
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
über das Thema
|"Towards optimal feedback control of high-dimensional systems".
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
über das Thema
|"Optimal Control in vertical vehicle dynamics
– About singular event detection and impulsive system dynamics – ".
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
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
über das Thema
|"Switching control based on sparsity".
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
über das Thema
|"Null controllability of degenerate parabolic equations".
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
über das Thema
|"On the Design of Predictive Controllers Based on Turnpike Properties".
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 . 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.
D.A. Carlson, A. Haurie, and A. Leizarowitz. (1991).
Infinite Horizon Optimal Control: Deterministic and Stochastic Systems.
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.
L. McKenzie. Turnpike theory.
Econometrica: Journal of the Econometric Society, 1976, 44(5), 841–865.
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.
L. Grüne. Economic receding horizon control without terminal constraints.
Automatica, 2013, 49, 725-734.
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
über das Thema
|"Controllability of Ensembles
of Linear Dynamical Systems".
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.
Prof. Dr. Mario Bebendorf
Prof. Dr. Kurt Chudej
Prof. Dr. Lars Grüne
Prof. Dr. Anton Schiela