Publications

Peter Benner, Jan Heiland (2023). Space and Chaos-Expansion Galerkin POD Low-order Discretization of PDEs for Uncertainty Quantification. Int. J. Numer. Methods Eng. (to appear).

Yongho Kim, Jan Heiland (2023). Convolutional Autoencoders, Clustering, and POD for Low-dimensional Parametrization of Navier-Stokes Equations.

Peter Benner, Jan Heiland, Steffen W. R. Werner (2023). A low-rank solution method for Riccati equations with indefinite quadratic terms. Numerical Algorithms.

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Peter Benner, Jan Heiland, Steffen W. R. Werner (2022). Robust output-feedback stabilization for incompressible flows using low-dimensional H∞-controllers. Comput. Optim. Appl..

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Peter Benner, Pawan Goyal, Jan Heiland, Igor Pontes Duff (2022). Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows. Electron. Trans. Numer. Anal..

Jan Heiland, Benjamin Unger (2022). Identification of Linear Time-Invariant Systems with Dynamic Mode Decomposition. MDPI Mathematics.

Jan Heiland, Peter Benner, Rezvan Bahmani (2022). Convolutional Neural Networks for Very Low-Dimensional LPV Approximations of Incompressible Navier-Stokes Equations. Frontiers Appl. Math. Stat..

Jan Heiland, Yongho Kim (2022). Convolutional Autoencoders and Clustering for Low-dimensional Parametrization of Incompressible Flows. IFAC-PapersOnLine.

Jan Heiland (2022). Convergence of Coprime Factor Perturbations for Robust Stabilization of Oseen Systems. Math. Control Relat. Fields.

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Peter Benner, Pawan Goyal, Jan Heiland, Igor Pontes (2022). A quadratic decoder approach to nonintrusive reduced-order modeling of nonlinear dynamical systems.

Peter Benner, Jan Heiland, Steffen W. R. Werner (2022). A low-rank solution method for Riccati equations with indefinite quadratic terms. Numerical Algorithms.

Maximilian Behr, Peter Benner, Jan Heiland (2021). Invariant Galerkin Ansatz Spaces and Davison-Maki Methods for the Numerical Solution of Differential Riccati Equations. Applied Mathematics and Computation.

Jan Heiland, Enrique Zuazua (2021). Classical System Theory Revisited for Turnpike in Standard State Space Systems and Impulse Controllable Descriptor Systems. SIAM J. Control Optim..

Peter Benner, Jan Heiland (2020). Space and Chaos-Expansion Galerkin POD Low-order Discretization of PDEs for Uncertainty Quantification. arXiv e-prints.

Chayan Bhawal, Jan Heiland, Peter Benner (2020). PD controllers to solve single-input, index-1 DAE based LQR problems. 2020 European Control Conference (ECC).

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Jens Bremer, Jan Heiland, Peter Benner, Kai Sundmacher (2020). Non-intrusive Time Galerkin POD for Optimal Control of a Fixed-Bed Reactor for CO2 Methanation. IFAC-PapersOnLine.

Peter Benner, Jan Heiland (2020). Equivalence of Riccati-based Robust Controller Design for Index-1 Descriptor Systems and Standard Plants with Feedthrough. 2020 European Control Conference (ECC).

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Xin Du, Yi Yang, Jan Heiland, Kaynyak Okyay (2019). Frequency-selective Filter Based Frequency Separated Feedback Control of Linear Systems: State Feedback Case. 2019 Chinese Control Conference (CCC).

Maximilian Behr, Peter Benner, Jan Heiland (2019). Solution Formulas for Differential Sylvester and Lyapunov Equations. Calcolo.

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Peter Benner, Jan Heiland, Steffen W. R. Werner (2019). Robust Controller versus Numerical Model Uncertainties for Stabilization of Navier-Stokes Equations. IFAC-PapersOnLine 52(2): 3rd IFAC Workshop on Control of Systems Governed by Partial Differential Equations CPDE 2019.

Henry von Wahl, Thomas Richter, Christoph Lehrenfeld, Jan Heiland, Piotr Minakowski (2019). Numerical benchmarking of fluid-rigid body interactions. Computers & Fluids.

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Robert Altmann, Jan Heiland (2019). Continuous, Semi-discrete, and Fully Discretized Navier-Stokes Equations. Applications of Differential-Algebraic Equations: Examples and Benchmarks.

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Manuel Baumann, Peter Benner, Jan Heiland (2018). Space-Time Galerkin POD with Application in Optimal Control of Semi-linear Parabolic Partial Differential Equations. SIAM Journal. Sci. Comput..

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Robert Altmann, Jan Heiland (2018). Regularization and Rothe Discretization of Semi-Explicit Operator DAEs. Int. J. Numer. Anal. Model.

Björn Baran, Peter Benner, Jan Heiland, Jens Saak (2018). Optimal Control of a Stefan Problem Fully Coupled with Navier-Stokes-Equations and Mesh Movement. Analele Stiintifice ale Universitatii Ovidius Constanta - Seria Matematica.

Peter Benner, Jan Heiland (2018). Exponential Stability and Stabilization of Extended Linearizations via Continuous Updates of Riccati Based Feedback. Internat. J. Robust Nonlinear Control.

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Peter Benner, Jan Heiland (2017). Nonlinear feedback stabilization of incompressible flows via updated Riccati-based gains. 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

Maximilian Behr, Peter Benner, Jan Heiland (2017). Example Setups of Navier- Stokes Equations with Control and Observation: Spatial Discretization and Representation via Linear-quadratic Matrix Coefficients. ArXiv e-prints.

Robert Altmann, Jan Heiland (2017). Simulation of multibody systems with servo constraints through optimal control. Multibody System Dynamics.

Mahmad I. Ahmad, Peter Benner, Pawan Goyal, Jan Heiland (2017). Moment-Matching Based Model Reduction for Navier-Stokes Type Quadratic-Bilinear Descriptor Systems. Z. Angew. Math. Mech..

Peter Benner, Jan Heiland (2017). Convergence of Approximations to Riccati-based Boundary-feedback Stabilization of Laminar Flows. IFAC-PapersOnLine 50(1): 20th IFAC World Congress.

Peter Benner, Jan Heiland (2016). Robust Stabilization of Laminar Flows in Varying Flow Regimes. IFAC-PapersOnLine 49(8): 2nd IFAC Workshop on Control of Systems Governed by Partial Differential Equations CPDE 2016.

Jörg Fehr, Jan Heiland, Christian Himpe, Jens Saak (2016). Best Practices for Replicability, Reproducibility and Reusability of Computer-Based Experiments Exemplified by Model Reduction Software. AIMS Mathematics.

Jan Heiland (2016). A Differential-Algebraic Riccati Equation for Applications in Flow Control. SIAM J. Control Optim..

Robert Altmann, Jan Heiland (2015). Finite Element Decomposition and Minimal Extension for Flow Equations. ESAIM: M2AN.

Robert Altmann, Jan Heiland (2015). Wie steuert man einen Kran?. Snapshots of modern mathematics from Oberwolfach.

Peter Benner, Jan Heiland (2015). Time-dependent Dirichlet Conditions in Finite Element Discretizations. ScienceOpen Research.

Peter Benner, Jan Heiland (2015). LQG-Balanced Truncation Low-Order Controller for Stabilization of Laminar Flows. Active Flow and Combustion Control 2014.

Manuel Baumann, Jan Heiland, Michael Schmidt (2015). Discrete Input/Output Maps and their Relation to Proper Orthogonal Decomposition. Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory.

Jan Heiland (2013). Decoupling, Semi-Discretization, and Optimal Control of Semi-linear Semi-explicit Index-2 Abstract Differential-Algebraic Equations and Application in Optimal Flow Control.

Jan Heiland, Volker Mehrmann (2012). Distributed Control of Linearized Navier-Stokes Equations via Discretized Input/Output Maps. Z. Angew. Math. Mech..

Jan Heiland, Volker Mehrmann, Michael Schmidt (2010). Systematic Discretization of Input/Output Maps and Control of Partial Differential Equations. Mathematical Methods, Models and Algorithms in Science and Technology.

Jan Heiland, Manuel Baumann, Astrid Walle, Volker Mehrmann, Michael Schäfer (2010). Simulation and Control of Drop Size Distributions in Stirred Liquid/Liquid Systems. Proc. 4th International Conference on Population Balance Modelling, September 15-17 2010, Berlin, Germany.

Jan Heiland, Volker Mehrmann, Michael Schmidt (2010). A New Discretization Framework for Input/Output Maps and its Application to Flow Control. Active Flow Control. Papers contributed to the Conference “Active Flow Control II 2010”, Berlin, Germany, May 26 to 28, 2010.

Astrid Herbst, Johannes Mauss, Jan Heiland, Alexander Orellano (2009). Shape Optimization in Train Aerodynamics. Proceedings of Euromech Colloquium 509 Vehicle Dynamics.

Jan Heiland (2009). Distributed Control of Semidiscretized Oseen Equations.