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Research Group Computational Methods in Systems and Control Theory

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Research Activities by Project Areas

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Model Order Reduction

Model Reduction for Mechanical Systems

Structural models of mechanical systems usually appear in the form of second order ODEs. Most MOR approaches rewrite these into first order form and thus derive first order reduced order models (ROMs). Here we focus on the exploitation of the second order structure and the generation of second order ROMs.
Coordinator: Dr. J. Saak

Title Scientist Funding Period
Model order reduction for thermo-elastic assembly group models Dr. J. Saak,
N. Lang
DFG SFB/Transregio 96 since 07/2011
Model Reduction for Mechanical Systems with Piezo Actuators M. M. Uddin
Dr. J. Saak
MPI, Chemnitz UT,
Fraunhofer IWU (Dresden)
since 09/2010

Parametric Model Reduction

We develop new methods for parameter-preserving model reduction, which are based on interpolation as well as hybrid techniques using system-theoretic approaches together with partial interpolation. These approaches efficiently reduce the large dimension of parameter-dependent systems as they arise in several application areas, e.g. in microsystems technology.
Coordinator: Dr. L. Feng

Multivariate Interpolation Methods for Parametric Model Reduction
(Model Reduction of Bilinear Systems)
T. Breiten MPI
since 01/2010
since 01/2012
Interpolatory Methods for Parametric Model Reduction Prof. P. Benner
Dr. U. Baur
MPI, Virgina Tech since 02/2009
Parametric MOR for Thermal Problems A. Bruns Bosch since 06/2011

Model Reduction for Micro- and Nanotechnical Systems

In this research area different model order reduction methods for the design of micro- and nanoscale integrated circuits and systems are developed. Special requirements are the consideration of linear systems with many input and output terminals, the analysis of the electromagnetic influence described by Maxwell's equations using uncertainty quantification and the treatment of nonlinear models.
Coordinator: Prof. P. Benner

MoreSim4Nano Model reduction for fast simulation of new semiconductor structures within nanotechnology and microsystems technology J. Schneider,
Dr. U. Baur
BMBF since 01/2011
Reduced Basis Methods for Electromagnetic Problems M. Heß MPI since 01/2011

Model Reduction of Nonlinear Systems

On the one hand, we investigate the application of snapshot- based methods (POD, RB) for application in highly nonlinear systems in process engineering applications. On the other hand, we develop a new methodology which is not snapshot- based and thus free of selecting training inputs. The reduced- order models will therefore be applicable under a wider range of operation conditions.
Coordinator: Prof. P. Benner

MOR by Rewriting to (Quadratic-)Bilinear System Order Reduction T. Breiten MPI since 01/2011
Model Order Reduction for Chromatographic Processes Dr. L. Feng,
Y. Zhang,
Dr. S. Li
MPI (with PCF group) since 04/2011
Dynamic, Analysis and Control of Anaerobic Digestions Processes for Biogas Production T. Breiten MPI (with PSE group) since 11/2010

Scientific Computing

Numerical (Multi-)Linear Algebra

We study linear and nonlinear eigenvalue problems with special structures arising in control, boundary element methods, or molecular dynamics. Moreover, we investigate the solution of special linear systems of equations arising in PDE control and MOR algorithms.
Coordinator: Dr. M. Stoll

TitleScientist FundingPeriod
Efficient Solution and Preconditioning of Linear Systems Dr. M. Stoll MPI, ESF OPTPDE since 10/2011
Large Scale Matrix Equations Prof. P. Benner,
M. Köhler,
Dr. J. Saak
MPI since 04/2010
Large Scale and Nonlinear Eigenvalue Problems Prof. P. Benner,
Université du Littoral Cote d'Opale
since 06/2010
since 08/2011
Fast solvers for phase field models Dr. M. Stoll,
J. Bosch
MPI since 01/2012

High Performance Computing

We investigate the parallel solution of the numerical problems related to the projects of the research group. The applications range from shared memory parallelization on modern multi- core CPU workstations and graphics processors to massively parallel approaches employing the new Linux Cluster otto of the Institute.
Coordinator: Dr. Jens Saak

TitleScientist FundingPeriod
Poweraware Scientific Computing Dr. A. Remón MPI
UJI Castellon
seit 05/2013
Development of Parallel Software Libraries (M.E.S.S.) Prof. P. Benner,
M. Köhler,
Dr. J. Saak
MPI since 10/2007
Multicore and (Multi-)GPU Computing M. Köhler,
Dr. J. Saak,
Dr. A. Remön
MPI since 10/2009
Linux Cluster otto Prof. P. Benner,
M. Köhler,
Dr. J. Saak
MPI since 05/2010
HPC solvers for PDE-constrained optimization Dr. M. Stoll,
Dr. A. Barker
MPI since 01/2013

Computer Aided Control Systems Design (CACSD)

Numerical Methods for Control Systems

This research topic mainly deals with numerical algorithms for robust control and stabilization of descriptor systems. One focus is the construction of (sub-)optimal H-infinity controllers or the computation of system norms by using spectral information of certain structured matrix pencils. Another important point is the development of efficient and robust software to solve these problems.
Coordinator: Prof. P. Benner

Title Scientist Funding Period
Numerical algorithms for generalized eigenvalue problems of even structure with application in robust control of descriptor systems Dr. P. Losse,
M. Voigt
TU Berlin
since 08/2010
Development of the Systems and Control Library SLICOT M. Voigt SynOptio GmbH since 02/2011
Periodic Control Systems: Analysis, Efficient Model Reduction and Development of Numerical Algorithms Dr. M. S. Hossain
J. Denißen
MPI since 09/2011
Optimal Damping of Vibrating Systems P. Kürschner
M. Voigt
J. Denißen
DAAD since 01/2013
Control and Stabilization of multiple pendulums P. Kürschner
C. Miller
D. M. Venkat
MPI since 2012

Control of Partial Differential Equations

Our team focuses on the numerical aspects of optimal control problems with PDE constraints. We concentrate on the efficient solution of the underlying matrix equations in the form of linear saddle point systems or matrix Riccati equations.
Coordinator: Dr. Martin Stoll

Title Scientist Funding Period
All-at-Once Solution of PDE Constrained Optimization Problems Dr. M. Stoll MPI since 05/2011
Solution of the Inverse Heat Conduction Problem (IHCP) using LQR Techniques N. Lang,
Dr. J. Saak
MPI, Fraunhofer IWU (Chemnitz) since 11/2010
Optimal Control-Based Feedback Stabilization in Multi-Field Flow Problems. H. Weichelt DFG priority programme 1253 since 11/2006
Boundary Feedback Stabilisation Using Non-Conforming Finite Elements H. Weichelt
Dr. J. Saak
Dr. P. Skryzpacz
MPI since 02/2012
Optimal Control of Chemical Processes Prof. Dr. P. Benner
Dr. M. Stoll
Dr. H. Yücel
MPI since 10/2012

Concluded Projects

Title Scientist Funding Period
Algorithms for Rank and Tensor Structured Matrices T. Mach MPI, Free State of Saxony 05/2008-06/2012
Simulation of the Glyphosate Aerial Spray Drift at the Ecuador-Colombia border Dr. J. Saak,
Dr. R. Schneider
SENACYT (Ecuadorian National Organization of Science), EPN Quito (Ecuador) 07/2009-12/2011
Modern model reduction methods for elastic components in the simulation of flexible multi body systems Dr. J. Saak,
P. Kürschner
Forschungsvereinigung Verbrennungskraftmaschinen e.V. 02/2010-12/2011
SyreNe System Reduction for Nanoscale IC Design A. Schneider,
T. Mach,
Dr. U. Baur,
M. Sahadet Hossain
BMBF 07/2007-12/2010
Numerical Solution of Optimal Control Problems with Instationary Diffusion-Convection and Diffusion-Reaction Equations Dr. S. Hein,
Dr. J. Saak,
Dr. H. Mena
DFG 01/2006-09/2010
Adaptive mesh refinement for Riccati equation based optimal control of PDEs Dr. R. Schneider TU-Chemnitz 01/2008-05/2010
Integrated Simulation of the System "Machine Tool - Actuation - Stock Removal Process" based on Model Order Reduction of the Structural FEM Model Dr. J. Saak DFG, MPI, iwb (TU Munich), Chemnitz University of Technology 01/2007-2/2010
O-MOORE-NICE! Operational MOdel Order REduction for Nanoscale IC Electronics Dr. M. Striebel EU Marie Curie Industry Host Fellowships 02/2007-01/2010
Automatic anisotropic mesh refinement for FEM Dr. R. Schneider TU-Chemnitz 10/2005-05/2010
Automatic, Parameter-Preserving Model Reduction for Applications in Microsystems Technology. Dr. U. Baur
Dr. L. Feng
DFG 10/2006-12/2009
Parallel algorithms for large-scale sparse algebraic Riccati equations and application in control
within DAAD programme "Acciones Integradas Hispano-Alemanas"
Dr. J. Saak DAAD 2006-2007
Integration of system-theoretic methods in model reduction into simulation tool for the development of electric circuits A. Schneider
T. Rothaug
R. Günzel
TU-Chemnitz, Infineon Technologies AG 08/2005-06/2006
Parallel numerical solution of optimal control problems with instationary diffusion-convection-reaction equations
(SFB393 project A15)
Prof. P. Benner,
Dr. J. Saak
TU-Chemnitz 10/2003 - 12/2005
Numerical Algorithms for Matrix Equations and Structured Eigenvalue Problems
Promotion of scientific exchange between scientists in Germany and scientists in Middle and Eastern Europe
Prof. P. Benner,
Dr. V. Sima
Numerical methods for robust control DFG 6/2002 - 3/2005
Calculation of torsional vibrations for gear train control assemblies in combustion engines
Cooperation with Ingenieursgesellschaft Auto und Verkehr (IAV GmbH)
04/2004 - 10/2004
Model reduction for large-scale systems in control and circuit simulation Dr. U. Baur DFG project D1 06/2002 - 09/2004

Jens Saak, jens.saak@mathematik.tu-chemnitz.de