Modeling, Simulation, and Optimization of Real Processes

Prof. Dr. Tobias Breiten

Faculty II - Mathematics and Natural Sciences
Institute of Mathematics, Sekr. MA 4-4
Technische Universität Berlin
Straße des 17. Juni 136
10623 Berlin

Office MA 577
Tel.: +49 - (0)30 - 314-79688
Email: tobias.breiten(at)tu-berlin.de

Office Hour
Tuesday, 12:30 - 13:30 (in MA 577)
Zoom-meetings on request per email

Teaching

Current courses (winter term 2023/24)

  • Numerical Mathematics II for Engineers - To the ISIS-page
  • Infinite-dimensional Control Theory - To the ISIS-page
  • Seminar Control and Optimization - To the ISIS-page

Here you can find additional information and concluded courses

Research Projects

  • Structute-preserving model reduction for the efficient computation of exceptional points in thermoacoustic spectra
    Daedalus-Project with Alessandro Borghi, more on that on the project page
  • Model reduction for multiple transported fronts with topological changes
    Daedalus-Project with Shubhaditya Burela, more on that on the project page
  • Nonlinear observer design - a data-driven optimal control perspective
    DFG-Project with Jesper Schröder, more on that on the project page
  • Structured optimal control of port-Hamiltonian network models
    SFB TRR 154-Project with Attila Karsai, more on that on the project page

Short CV

11/2009Diploma in Technomathematik, Technische Universität Kaiserslautern, Germany
04/2013PhD in mathematics, Otto-von-Guericke-Universität und Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
10/2013Assistant professor, Karl-Franzens-Universität Graz, Austria
06/2018Habilitation in mathematics, Karl-Franzens-Universität Graz, Austria
05/2019Associate professor, Karl-Franzens-Universität Graz, Austria
04/2020Juniorprofessor TU Berlin, Germany
08/2022Professor TU Berlin, Germany

Secretary's Office

Alexandra Schulte
MA 4-4
Office 572
Tel: +49 (0)30 314-28579 oder 01520 / 361 96 10 (contact via WhatsApp possible)
Fax: +49 (0) 30 314 - 2 89 67
Email: schulte(at)math.tu-berlin.de

Publications

2023

Articles
Borghi, Alessandro; Breiten, Tobias
H2 optimal model reduction on general domains
2023
Breiten, Tobias; Kunisch, Karl
Improving the Convergence Rates for the Kinetic Fokker-Planck Equation by Optimal Control
SIAM Journal on Control and Optimization, 61 :1557-1581
2023
Breiten, Tobias; Schröder, Jesper
Local well-posedness of the Mortensen observer
2023
Breiten, Tobias; Kunisch, Karl; Schröder, Jesper
Numerical realization of the Mortensen observer via a Hessian-augmented polynomial approximation of the value function
2023
Breiten, Tobias; Höveler, Bernhard
On the approximability of Koopman-based operator Lyapunov equations
SIAM Journal on Control and Optimization
2023
Breiten, Tobias; Karsai, Attila
Structure-preserving H∞ Control for Port-Hamiltonian Systems
System & Control Letters, 174:105493
2023

2022

Breiten, Tobias; Morandin, Riccardo; Schulze, Philipp
Error bounds for port-Hamiltonian model and controller reduction based on system balancing
Computers & Mathematics with Applications, 116 :100-115
2022
ISSN: 0898-1221
Breiten, Tobias; Unger, Benjamin
Passivity preserving model reduction via spectral factorization
Automatica, 142 :110368
2022
ISSN: 0005-1098
Breiten, Tobias; Hinsen, Dorothea; Unger, Benjamin
Towards a modeling class for port-Hamiltonian systems with time-delay
2022

2021

Contribution to Books
Breiten, Tobias; Stykel, Tatjana
Balancing-related methods
In P. Benner, S. Grivet-Talocia, A. Quarteroni, G. Rozza, W. Schilder, L. M. Silveira, Editor
Publisher: De Gruyter
Volume 1: System- and Data-Driven Methods and Algorithms Edition
2021
Books
Benner, Peter; Breiten, Tobias; Faßbender, Heike; Hinze, Michael; Stykel, Tatjana; Zimmermann, Ralf
Model Reduction of Complex Dynamical Systems
Publisher: Birkhäuser/Springer
171. Edition
2021
ISBN
978-3-030-72982-0
Articles
Breiten, Tobias; Schulze, Philipp
Structure-Preserving Linear Quadratic Gaussian Balanced Truncation for Port-Hamiltonian Descriptor Systems
2021
Breiten, Tobias; Hartmann, Carsten; Neureither, Lara; Sharma, Upanshu
Stochastic gradient descent and fast relaxation to thermodynamic equilibrium: a stochastic control approach
Journal of Mathematical Physics, 62 (12)
2021
Breiten, Tobias; Dolgov, Sergey; Stoll, Martin
Solving differential Riccati equations: A nonlinear space-time method using tensor trains
Numerical Algebra, Control & Optimization, 11 (3) :407–429
2021
Breiten, Tobias; Kunisch, Karl
Neural network based nonlinear observers
Systems & Control Letters, 148 :104829
2021
ISSN: 0167-6911
Berger, Thomas; Breiten, Tobias; Puche, Marc; Reis, Timo
Funnel control for the monodomain equations with the FitzHugh-Nagumo model
Journal of Differential Equations, 286 :164-214
2021
ISSN: 0022-0396

2020

Breiten, Tobias; Kunisch, Karl
Feedback Stabilization of the Three-Dimensional Navier-Stokes Equations using Generalized Lyapunov Equations
Discrete and Continuous Dynamical Systems - Series A, 40 (7) :4197–4229
2020
Benner, Peter; Breiten, Tobias; Hartmann, Carsten; Schmidt, Burkhard
Model reduction of controlled Fokker-Planck and Liouville-von Neumann equations
Journal of Computational Dynamics, 7 (1) :1–3
2020
Breiten, Tobias; Pfeiffer, Laurent
On the Turnpike Property and the Receding-Horizon Method for Linear-Quadratic Optimal Control Problems
SIAM Journal on Control and Optimization, 58 (2) :1077-1102
2020
Contribution to Books
Breiten, Tobias; Beattie, Christopher; Gugercin, Serkan
H2-gap model reduction for stabilizable and detectable systems
In C. Beattie, P. Benner, M. Embree, S. Gugercin, S. Lefteriu, Editor
Publisher: Springer
2020

2019

Articles
Breiten, Tobias; Kunisch, Karl; Pfeiffer, Laurent
Feedback Stabilization of the Two-Dimensional Navier-Stokes Equations by Value Function Approximation
Applied Mathematics & Optimization, 80 (3) :599–641
2019
Breiten, Tobias; Ringh, Emil
Residual-based iterations for the generalized Lyapunov equation
BIT Numerical Mathematics, 59 :823–852
2019
Breiten, Tobias; Kunisch, Karl; Pfeiffer, Laurent
Taylor Expansions of the Value Function Associated with a Bilinear Optimal Control Problem
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 36 (5) :1361–1399
2019

2018

Breiten, Tobias; Kunisch, Karl; Pfeiffer, Laurent
Numerical Study of Polynomial Feedback Laws for a Bilinear Control Problem
Mathematical Control and Related Fields, 8 (3\&4) :557–582
2018
Breiten, Tobias; Kunisch, Karl; Pfeiffer, Laurent
Infinite-Horizon Bilinear Optimal Control Problems: Sensitivity Analysis and Polynomial Feedback Laws
SIAM Journal on Control and Optimization, 56 (5) :3184-3214
2018
Breiten, Tobias; Kunisch, Karl; Pfeiffer, Laurent
Control strategies for the Fokker-Planck equation
ESAIM: COCV, 24 (2) :741-763
2018

2017

Breiten, Tobias; Kunisch, Karl
Boundary Feedback Stabilization of the Monodomain Equations
Mathematical Control and Related Fields, 7 (3) :369–391
2017
Breiten, Tobias; Kunisch, Karl
Compensator design for the monodomain equations with the FitzHugh-Nagumo model
ESAIM: COCV, 23 (1) :241-262
2017
Breiten, Tobias; Kunisch, Karl; Rodrigues, Sérgio S.
Feedback Stabilization to Nonstationary Solutions of a Class of Reaction Diffusion Equations of FitzHugh–Nagumo Type
SIAM Journal on Control and Optimization, 55 (4) :2684-2713
2017
Conferences
Breiten, Tobias; Kunisch, Karl; Pfeiffer, Laurent
A reduction method for Riccati-based control of the Fokker-Planck equation
Volume 50, Page 1631-1636
2017
Contribution to Books
Benner, Peter; Breiten, Tobias
Model order reduction based on system balancing
In P. Benner, M. Ohlberger, A. Cohen, K. Willcox, Editor
Chapter Chapter 6, Page 261-295
Publisher: Society for Industrial and Applied Mathematics
2017
261-295

2016

Articles
Breiten, Tobias; Simoncini, V.; Stoll, Martin
Low-rank solvers for fractional differential equations
Electronic Transactions on Numerical Analysis, 45 :107-132
2016
Breiten, Tobias
Structure-Preserving Model Reduction for Integro-Differential Equations
SIAM Journal on Control and Optimization, 54 (6) :2992-3015
2016

2015

Contribution to Books
Benner, Peter; Breiten, Tobias; Feng, Lihong
Matrix equations and model reduction
In W. Gao, Z. Bai, Y. Su, Editor
Publisher: World Scientific
19. Edition
2015
Conferences
Breiten, Tobias; Kunisch, Karl
Feedback stabilization of the Schlögl model by LQG-balanced truncation
2015 European Control Conference (ECC), Page 1171-1176
2015
Articles
Benner, Peter; Breiten, Tobias
Two-Sided Projection Methods for Nonlinear Model Order Reduction
SIAM Journal on Scientific Computing, 37 (2) :B239-B260
2015
Breiten, Tobias; Beattie, Christopher; Gugercin, Serkan
Near-optimal frequency-weighted interpolatory model reduction
Systems & Control Letters, 78 :8-18
2015
ISSN: 0167-6911
Stoll, Martin; Breiten, Tobias
A Low-Rank in Time Approach to PDE-Constrained Optimization
SIAM Journal on Scientific Computing, 37 (1) :B1-B29
2015

2014

Benner, Peter; Breiten, Tobias
On optimality of approximate low rank solutions of large-scale matrix equations
Systems & Control Letters, 67 :55-64
2014
ISSN: 0167-6911
Benner, Peter; Breiten, Tobias
Rational interpolation methods for symmetric Sylvester equations
Electronic Transactions on Numerical Analysis, 42 :147-164
2014
Breiten, Tobias; Kunisch, Karl
Riccati-Based Feedback Control of the Monodomain Equations With the Fitzhugh–Nagumo Model
SIAM Journal on Control and Optimization, 52 (6) :4057-4081
2014

2013

Benner, Peter; Breiten, Tobias
Low rank methods for a class of generalized Lyapunov equations and related issues
Numerische Mathematik, 124 (3) :441-470
2013

2012

Benner, Peter; Breiten, Tobias
Interpolation-Based \$H_2\$-Model Reduction of Bilinear Control Systems
SIAM Journal on Matrix Analysis and Applications, 33 (3) :859-885
2012
Conferences
Benner, Peter; Breiten, Tobias
Krylov-Subspace Based Model Reduction of Nonlinear Circuit Models Using Bilinear and Quadratic-Linear Approximations
Progress in Industrial Mathematics at ECMI 2010, Page 153–159
In Michael Günther and Andreas Bartel and Markus Brunk and Sebastian Schöps and Michael Striebel, Editor
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg
2012
ISBN
978-3-642-25100-9

2011

Articles
Benner, Peter; Breiten, Tobias; Damm, T.
Generalised tangential interpolation for model reduction of discrete-time MIMO bilinear systems
International Journal of Control, 84 (8) :1398-1407
2011
Publisher: Taylor & Francis
Conferences
Benner, Peter; Breiten, Tobias
On H2-model reduction of linear parameter-varying systems
Volume 11, Page 805-806
2011

2010

Articles
Breiten, Tobias; Damm, Tobias
Krylov subspace methods for model order reduction of bilinear control systems
Systems & Control Letters, 59 (8) :443-450
2010
ISSN: 0167-6911
Conferences
Benner, Peter; Breiten, Tobias; Damm, Tobias
Krylov Subspace Methods for Model Order Reduction of Bilinear Discrete-Time Control Systems
Volume 10, Page 601-602
2010