45 citations · 165 across the 20 of their papers we have counts for
21 papers
MaRDIFlow: A CSE workflow framework for abstracting meta-data from FAIR computational experiments
Pavan L. Veluvali, Jan Heiland, Peter Benner
Numerical algorithms and computational tools are instrumental in navigating and addressing complex simulation and data processing tasks. The exponential growth of metadata and para…
Frequency-dependent Switching Control for Disturbance Attenuation of Linear Systems
Jingjing Zhang, Jan Heiland, Peter Benner +1
The generalized Kalman-Yakubovich-Popov lemma as established by Iwasaki and Hara in 2005 marks a milestone in the analysis and synthesis of linear systems from a finite-frequency p…
Low-complexity linear parameter-varying approximations of incompressible Navier-Stokes equations for truncated state-dependent Riccati feedback
Jan Heiland, Steffen W. R. Werner
Nonlinear feedback design via state-dependent Riccati equations is well established but unfeasible for large-scale systems because of computational costs. If the system can be embe…
Convolutional Autoencoders, Clustering and POD for Low-dimensional Parametrization of Navier-Stokes Equations
Yongho Kim, Jan Heiland
Simulations of large-scale dynamical systems require expensive computations. Low-dimensional parametrization of high-dimensional states such as Proper Orthogonal Decomposition (POD…
A quadratic decoder approach to nonintrusive reduced-order modeling of nonlinear dynamical systems
Peter Benner, Pawan Goyal, Jan Heiland +1
Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated…
Exponential Lag Synchronization of Cohen-Grossberg Neural Networks with Discrete and Distributed Delays on Time Scales
Vipin Kumar, Jan Heiland, Peter Benner
In this article, we investigate exponential lag synchronization results for the Cohen-Grossberg neural networks (C-GNNs) with discrete and distributed delays on an arbitrary time d…
A low-rank solution method for Riccati equations with indefinite quadratic terms
Peter Benner, Jan Heiland, Steffen W. R. Werner
Algebraic Riccati equations with indefinite quadratic terms play an important role in applications related to robust controller design. While there are many established approaches…
Identification of linear time-invariant systems with Dynamic Mode Decomposition
Jan Heiland, Benjamin Unger
Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identificati…
Robust output-feedback stabilization for incompressible flows using low-dimensional -controllers
Peter Benner, Jan Heiland, Steffen W. R. Werner
Output-based controllers are known to be fragile with respect to model uncertainties. The standard -control theory provides a general approach to robust contr…
Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows
Peter Benner, Pawan Goyal, Jan Heiland +1
Reduced-order modeling has a long tradition in computational fluid dynamics. The ever-increasing significance of data for the synthesis of low-order models is well reflected in the…
Space and Chaos-Expansion Galerkin POD Low-order Discretization of PDEs for Uncertainty Quantification
Peter Benner, Jan Heiland
The quantification of multivariate uncertainties in partial differential equations can easily exceed any computing capacity unless proper measures are taken to reduce the complexit…
Classical System Theory Revisited for Turnpike in Standard State Space Systems and Impulse Controllable Descriptor Systems
Jan Heiland, Enrique Zuazua
The concept of turnpike connects the solution of long but finite time horizon optimal control problems with steady state optimal controls. A key ingredient of the analysis of the t…
Convergence of Coprime Factor Perturbations for Robust Stabilization of Oseen Systems
Jan Heiland
Linearization based controllers for incompressible flows have been proven to work in theory and in simulations. To realize such a controller numerically, the infinite dimensional s…
Invariant Galerkin Ansatz Spaces and Davison-Maki Methods for the Numerical Solution of Differential Riccati Equations
Maximilian Behr, Peter Benner, Jan Heiland
The differential Riccati equation appears in different fields of applied mathematics like control and system theory. Recently Galerkin methods based on Krylov subspaces were develo…
Numerical benchmarking of fluid-rigid body interactions
Henry von Wahl, Thomas Richter, Christoph Lehrenfeld +2
We propose a fluid-rigid body interaction benchmark problem, consisting of a solid spherical obstacle in a Newtonian fluid, whose centre of mass is fixed but is free to rotate. A n…
Continuous, Semi-discrete, and Fully Discretized Navier-Stokes Equations
Robert Altmann, Jan Heiland
The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and tempor…
Solution Formulas for Differential Sylvester and Lyapunov Equations
Maximilian Behr, Peter Benner, Jan Heiland
The differential Sylvester equation and its symmetric version, the differential Lyapunov equation, appear in different fields of applied mathematics like control theory, system the…
Example Setups of Navier-Stokes Equations with Control and Observation: Spatial Discretization and Representation via Linear-quadratic Matrix Coefficients
Maximilian Behr, Peter Benner, Jan Heiland
We provide spatial discretizations of nonlinear incompressible Navier-Stokes equations with inputs and outputs in the form of matrices ready to use in any numerical linear algebra…
Space-time Galerkin POD with application in optimal control of semi-linear parabolic partial differential equations
Manuel Baumann, Peter Benner, Jan Heiland
In the context of Galerkin discretizations of a partial differential equation (PDE), the modes of the classical method of Proper Orthogonal Decomposition (POD) can be interpreted a…
Exponential Stability and Stabilization of Extended Linearizations via Continuous Updates of Riccati Based Feedback
Peter Benner, Jan Heiland
Many recent works on stabilization of nonlinear systems target the case of locally stabilizing an unstable steady state solutions against small perturbation. In this work we explic…
Best Practices for Replicability, Reproducibility and Reusability of Computer-Based Experiments Exemplified by Model Reduction Software
Jörg Fehr, Jan Heiland, Christian Himpe +1
Over the recent years the importance of numerical experiments has gradually been more recognized. Nonetheless, sufficient documentation of how computational results have been obtai…