Mathematik, Arbeitsrichtung Modellierung, Simulation und Optimierung realer Prozesse
Prof. Dr. Tobias Breiten
Fakultät II - Mathematik und Naturwissenschaften
Institut für Mathematik, Sekr. MA 4-4
Technische Universität Berlin
Straße des 17. Juni 136
10623 Berlin
Raum MA 577
Tel.: +49 - (0)30 - 314-79688
Email: tobias.breiten(at)tu-berlin.de
Sprechstunde
Dienstag, 12:30 - 13:30 Uhr (in MA 577)
Alternativ Anfragen per Email für Zoom-Sprechstunden
Lehre
Aktuell (Wintersemester 2023/24)
- Numerische Mathematik II für Ingenieurswissenschaften - Zur ISIS-Seite
- Infinite-dimensional Control Theory - Zur ISIS-Seite
- Seminar Control and Optimization - Zur ISIS-Seite
Hier gibt es weitere Informationen und vergangene Lehrveranstaltungen
Forschungsprojekte
- Strukturerhaltende Modellreduktion für die effiziente Berechnung von defekten Eigenwerten in thermoakustischen Spektren
Daedalus-Projekt mit Alessandro Borghi, mehr dazu auf der Projektseite - Modellreduktion für mehrere bewegte Fronten mit topologischen Veränderungen
Daedalus-Projekt mit Shubhaditya Burela, mehr dazu auf der Projektseite - Entwurf nichtlinearer Beobachter - eine datengesteuerte Perspektive der optimalen Steuerung
DFG-Projekt mit Jesper Schröder, mehr dazu auf der Projektseite - Strukturiere Steuerung und Regelung von port-Hamiltonischen Netzwerkmodellen
SFB TRR 154-Projekt mit Attila Karsai, mehr dazu auf der Projektseite
Kurzlebenslauf
| 11/2009 | Diplom in Technomathematik, Technische Universität Kaiserslautern, Deutschland |
| 04/2013 | PhD in Mathematik, Otto-von-Guericke-Universität und Max-Planck-Institut für Dynamik komplexer technischer Systeme, Magdeburg, Deutschland |
| 10/2013 | Assistenzprofessor, Karl-Franzens-Universität Graz, Österreich |
| 06/2018 | Habilitation in Mathematik, Karl-Franzens-Universität Graz, Österreich |
| 05/2019 | Assoziierter Professor, Karl-Franzens-Universität Graz, Österreich |
| 04/2020 | Juniorprofessor TU Berlin, Deutschland |
| 08/2022 | Professor TU Berlin, Deutschland |
© Felix Noak
Sekretariat
| Alexandra Schulte |
| MA 4-4 |
| Raum 572 |
| Tel: +49 (0)30 314-28579 oder 01520 / 361 96 10 (auch WhatsApp) |
| Fax: +49 (0) 30 314 - 2 89 67 |
| Email: schulte(at)math.tu-berlin.de |
Publikationen
2023
Artikel
Borghi,
Alessandro;
Breiten,
Tobias
H2 optimal model reduction on general domains
2023
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
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
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
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
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
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
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
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
Towards a modeling class for port-Hamiltonian systems with time-delay
2022
2021
Buchbeiträge
Breiten,
Tobias;
Stykel,
Tatjana
Balancing-related methods
In P. Benner, S. Grivet-Talocia, A. Quarteroni, G. Rozza, W. Schilder, L. M. Silveira, Editor
Herausgeber: De Gruyter
Volume 1: System- and Data-Driven Methods and Algorithms Edition
2021
Balancing-related methods
In P. Benner, S. Grivet-Talocia, A. Quarteroni, G. Rozza, W. Schilder, L. M. Silveira, Editor
Herausgeber: De Gruyter
Volume 1: System- and Data-Driven Methods and Algorithms Edition
2021
Bücher
Benner,
Peter;
Breiten,
Tobias;
Faßbender,
Heike;
Hinze,
Michael;
Stykel,
Tatjana;
Zimmermann,
Ralf
Model Reduction of Complex Dynamical Systems
Herausgeber: Birkhäuser/Springer
171. Edition
2021
Model Reduction of Complex Dynamical Systems
Herausgeber: Birkhäuser/Springer
171. Edition
2021
- ISBN
- 978-3-030-72982-0
Artikel
Breiten,
Tobias;
Schulze,
Philipp
Structure-Preserving Linear Quadratic Gaussian Balanced Truncation for Port-Hamiltonian Descriptor Systems
2021
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
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
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
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
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
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
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
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
Buchbeiträge
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
Herausgeber: Springer
2020
H2-gap model reduction for stabilizable and detectable systems
In C. Beattie, P. Benner, M. Embree, S. Gugercin, S. Lefteriu, Editor
Herausgeber: Springer
2020
2019
Artikel
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
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
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
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
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
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
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
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
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
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
Konferenzen
Breiten,
Tobias;
Kunisch,
Karl;
Pfeiffer,
Laurent
A reduction method for Riccati-based control of the Fokker-Planck equation
Band 50, Seite 1631-1636
2017
A reduction method for Riccati-based control of the Fokker-Planck equation
Band 50, Seite 1631-1636
2017
Buchbeiträge
Benner,
Peter;
Breiten,
Tobias
Model order reduction based on system balancing
In P. Benner, M. Ohlberger, A. Cohen, K. Willcox, Editor
Kapitel Chapter 6, Seite 261-295
Herausgeber: Society for Industrial and Applied Mathematics
2017
261-295
Model order reduction based on system balancing
In P. Benner, M. Ohlberger, A. Cohen, K. Willcox, Editor
Kapitel Chapter 6, Seite 261-295
Herausgeber: Society for Industrial and Applied Mathematics
2017
261-295
2016
Artikel
Breiten,
Tobias;
Simoncini,
V.;
Stoll,
Martin
Low-rank solvers for fractional differential equations
Electronic Transactions on Numerical Analysis, 45 :107-132
2016
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
Structure-Preserving Model Reduction for Integro-Differential Equations
SIAM Journal on Control and Optimization, 54 (6) :2992-3015
2016
2015
Buchbeiträge
Benner,
Peter;
Breiten,
Tobias;
Feng,
Lihong
Matrix equations and model reduction
In W. Gao, Z. Bai, Y. Su, Editor
Herausgeber: World Scientific
19. Edition
2015
Matrix equations and model reduction
In W. Gao, Z. Bai, Y. Su, Editor
Herausgeber: World Scientific
19. Edition
2015
Konferenzen
Breiten,
Tobias;
Kunisch,
Karl
Feedback stabilization of the Schlögl model by LQG-balanced truncation
2015 European Control Conference (ECC), Seite 1171-1176
2015
Feedback stabilization of the Schlögl model by LQG-balanced truncation
2015 European Control Conference (ECC), Seite 1171-1176
2015
Artikel
Benner,
Peter;
Breiten,
Tobias
Two-Sided Projection Methods for Nonlinear Model Order Reduction
SIAM Journal on Scientific Computing, 37 (2) :B239-B260
2015
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
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
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
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
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
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
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
Interpolation-Based \$H_2\$-Model Reduction of Bilinear Control Systems
SIAM Journal on Matrix Analysis and Applications, 33 (3) :859-885
2012
Konferenzen
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, Seite 153–159
In Michael Günther and Andreas Bartel and Markus Brunk and Sebastian Schöps and Michael Striebel, Editor
Herausgeber: Springer Berlin Heidelberg, Berlin, Heidelberg
2012
Krylov-Subspace Based Model Reduction of Nonlinear Circuit Models Using Bilinear and Quadratic-Linear Approximations
Progress in Industrial Mathematics at ECMI 2010, Seite 153–159
In Michael Günther and Andreas Bartel and Markus Brunk and Sebastian Schöps and Michael Striebel, Editor
Herausgeber: Springer Berlin Heidelberg, Berlin, Heidelberg
2012
- ISBN
- 978-3-642-25100-9
2011
Artikel
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
Herausgeber: Taylor & Francis
Generalised tangential interpolation for model reduction of discrete-time MIMO bilinear systems
International Journal of Control, 84 (8) :1398-1407
2011
Herausgeber: Taylor & Francis
Konferenzen
Benner,
Peter;
Breiten,
Tobias
On H2-model reduction of linear parameter-varying systems
Band 11, Seite 805-806
2011
On H2-model reduction of linear parameter-varying systems
Band 11, Seite 805-806
2011
2010
Artikel
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
Krylov subspace methods for model order reduction of bilinear control systems
Systems & Control Letters, 59 (8) :443-450
2010
ISSN: 0167-6911
Konferenzen
Benner,
Peter;
Breiten,
Tobias;
Damm,
Tobias
Krylov Subspace Methods for Model Order Reduction of Bilinear Discrete-Time Control Systems
Band 10, Seite 601-602
2010
Krylov Subspace Methods for Model Order Reduction of Bilinear Discrete-Time Control Systems
Band 10, Seite 601-602
2010