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Inhalt des Dokuments

Veröffentlichungen

Eingereichte Arbeiten
T. Breiten and K. Kunisch
Neural network based nonlinear observers
arXiv:2003.07269
T. Berger, T. Breiten, M. Puche, and T. Reis
Funnel control for the monodomain equations with the FitzHugh-Nagumo model
arXiv:1909.0184
T. Breiten, C. Beattie, and S. Gugercin
ℋ₂-gap model reduction for stabilizable and detectable systems
arXiv:1909.13764
Begutachtete Artikel in Zeitschriften
T. Breiten, S. Dolgov, and M. Stoll
Solving differential Riccati equations: A nonlinear space-time method using tensor trains
Numerical Algebra, Control & Optimization, accepted, 2020.
arXiv:1912.06944

T. Breiten and K. Kunisch
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.
arXiv:1909.13757
Tobias Breiten, Laurent Pfeiffer
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.
arXiv:1811.02421.
Peter Benner, Tobias Breiten, Carsten Hartmann, Burkhard Schmidt
Model reduction of controlled Fokker-Planck and Liouville-von Neumann equations
Journal of Computational Dynamics, 7(1): 1-33, 2020.
arXiv:1706.09882
Tobias Breiten, Karl Kunisch, Laurent Pfeiffer
Feedback Stabilization of the Two-Dimensional Navier-Stokes Equations by Value Function Approximation
Applied Mathematics & Optimization, 80(3): 599-641, 2019.
arXiv:1902.00394
Tobias Breiten, Emil Ringh
Residual-based iterations for the generalized Lyapunov equation
BIT Numerical Mathematics 59(4) (2019), 823-852.
arXiv:1807.10715
Tobias Breiten, Karl Kunisch, Laurent Pfeiffer:
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) (2019), 1361-1399.
arXiv:1706.05341
Tobias Breiten, Karl Kunisch, Laurent Pfeiffer
Infinite-Horizon Bilinear Optimal Control Problems: Sensitivity Analysis and Polynomial Feedback Laws
SIAM Journal on Control and Optimization 56(5) (2018), 3184-3214.
Tobias Breiten, Karl Kunisch, Laurent Pfeiffer
Numerical Study of Polynomial Feedback Laws for a Bilinear Control Problem
Mathematical Control and Related Fields 8(3&4) (2018), 557-582.
arXiv:1709.04227
Tobias Breiten, Karl Kunisch, Laurent Pfeiffer
Control Strategies for the Fokker-Planck Equation
ESAIM: Control, Optimisation and Calculus of Variations 24(2) (2018), 741-763.
arXiv:1707.07510
Tobias Breiten, Karl Kunisch, Sergio Rodrigues
Feedback Stabilization to Non-Stationary Solutions of a Class of Reaction Diffusion Equations of Fitzhugh-Nagumo Type
SIAM Journal on Control and Optimization 55(4) (2017), 2684-2713.
Tobias Breiten, Karl Kunisch
Boundary Feedback Stabilization of the Monodomain Equations
Mathematical Control and Related Fields 7(3) (2017), 369-391
Tobias Breiten, Karl Kunisch
Compensator design for the monodomain equations with the FitzHugh-Nagumo model
ESAIM: Control, Optimisation and Calculus of Variations 23(1) (2017), 241-262.
Tobias Breiten
Structure-preserving model reduction for integro-differential equations
SIAM Journal on Control and Optimization 54(6) (2016), 2992-3015.
Tobias Breiten, Valeria Simoncini, Martin Stoll
Low-rank solvers for fractional differential equations
Electronic Transactions on Numerical Analysis 45 (2016), 107-132.
Tobias Breiten, Christopher Beattie, Serkan Gugercin
Near-optimal frequency-weighted interpolatory model reduction
Systems & Control Letters 78 (2015), 8-18.
arXiv:1309.0136
Peter Benner, Tobias Breiten
Two-sided projection methods for nonlinear model order reduction
SIAM Journal on Scientific Computing 37(2) (2015), B239-B260.
Martin Stoll, Tobias Breiten
A low-rank in time approach to PDE-constrained optimization
SIAM Journal on Scientific Computing 37(1) (2015), B1-B29.
Tobias Breiten, Karl Kunisch
Riccati-based feedback control of the monodomain equations with the FitzHugh-Nagumo model
SIAM Journal on Control and Optimization 52 (2014), 4057-4081.
Peter Benner, Tobias Breiten
Rational interpolation methods for symmetric Sylvester equations
Electronic Transactions on Numerical Analysis 42 (2014), 147-164.
Peter Benner, Tobias Breiten
On optimality of approximate low rank solutions of large-scale matrix equations
Systems & Control Letters 67 (2014), 55-64.
Peter Benner, Tobias Breiten
Low rank methods for a class of generalized Lyapunov equations and related issues
Numerische Mathematik 124 (2013), 441-470.
Peter Benner, Tobias Breiten
Interpolation-Based ℋ₂-Model Reduction of Bilinear Control Systems
SIAM Journal on Matrix Analysis and Applications 33 (2012), 859-885.
Peter Benner, Tobias Breiten, Tobias Damm
Generalised tangential interpolation for model reduction of discrete-time MIMO bilinear systems
International Journal of Control 84 (2011), 1398-1407.
Tobias Breiten, Tobias Damm
Krylov subspace methods for model order reduction of bilinear control systems
Systems & Control Letters 59 (2010), 443-450.
Begutachtete Artikel in Sammel- und Tagungsbänden
T. Breiten, K. Kunisch, and L. Pfeiffer
A reduction method for Riccati-based control of the Fokker-Planck equation
In 20th IFAC World Congress, volume 50, pages 1631–1636, 2017.
T. Breiten and K. Kunisch
Feedback stabilization of the Schlögl model by LQG-balanced truncation
In 2015 European Control Conference (ECC), pages 1171–1176, 2015.
P. Benner and T. Breiten
Krylov-subspace based model reduction of nonlinear circuit models using bilinear and quadratic-linear approximations
In Michael Günther, Andreas Bartel,Markus Brunk, Sebastian Schöps, and Michael Striebel, editors, Progress in Industrial Mathematics at ECMI 2010, volume 17 of Mathematics in Industry, pages 153–159.
Springer Berlin Heidelberg, 2012.
P. Benner and T. Breiten
On H2-model reduction of linear parameter-varying systems
In Proceedings in Applied Mathematics and Mechanics, volume 11, pages 805–806.
Wiley-VCH Verlag GmbH & Co, 2011.
P. Benner, T. Breiten, and T. Damm
Krylov subspace methods for model order reduction of bilinear discrete-time control systems
In Proceedings in Applied Mathematics and Mechanics, volume 10, pages 601–602.
Wiley-VCH Verlag GmbH & Co, 2010.
Buchkapitel
P. Benner and T. Breiten
Chapter 6: Model order reduction based on system balancing
In P. Benner, M. Ohlberger, A. Cohen, and K. Willcox, editors, Model Reduction and Approximation, pages 261–295.
Society for Industrial and Applied Mathematics, 2017.
P. Benner, T. Breiten, and L. Feng
Matrix equations and model reduction
In W. Gao, Z. Bai and Y. Su, editors, Matrix Functions and Matrix Equations, volume 19 of Series in Contemporary Applied Mathematics, pages 50–75.
World Scientific, 2015.
Qualifizierungsschriften
T. Breiten
Feedback control of nonlinear infinite-dimensional control systems
Cumulative habilitation thesis, University of Graz, 2018.
T. Breiten
Interpolatory Methods for Model Reduction of Large-Scale Dynamical Systems
Dissertation, Otto von Guericke University Magdeburg, 2013.
T. Breiten
Krylov subspace methods for model order reduction of bilinear control systems
Diplomarbeit, Department of Mathematics, Technical University of Kaiserslautern, 2009.

 

 

 

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