[图书][B] Model order reduction for PDE constrained optimization

P Benner, E Sachs, S Volkwein - 2014 - Springer
The optimization and control of systems governed by partial differential equations (PDEs)
usually requires numerous evaluations of the forward problem or the optimality system …

Deep model predictive flow control with limited sensor data and online learning

K Bieker, S Peitz, SL Brunton, JN Kutz… - … and computational fluid …, 2020 - Springer
The control of complex systems is of critical importance in many branches of science,
engineering, and industry, many of which are governed by nonlinear partial differential …

[图书][B] Model order reduction for differential-algebraic equations: a survey

P Benner, T Stykel - 2017 - Springer
In this paper, we discuss the model order reduction problem for descriptor systems, that is,
systems with dynamics described by differential-algebraic equations. We focus on linear …

Operator inference and physics-informed learning of low-dimensional models for incompressible flows

P Benner, P Goyal, J Heiland, IP Duff - arXiv preprint arXiv:2010.06701, 2020 - arxiv.org
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 …

A numerical comparison of different solvers for large-scale, continuous-time algebraic Riccati equations and LQR problems

P Benner, Z Bujanovic, P Kurschner, J Saak - SIAM Journal on Scientific …, 2020 - SIAM
In this paper, we discuss numerical methods for solving large-scale continuous-time
algebraic Riccati equations. These methods have been the focus of intensive research in …

Matrix Equations, Sparse Solvers: M-MESS-2.0.1—Philosophy, Features, and Application for (Parametric) Model Order Reduction

P Benner, M Köhler, J Saak - Model Reduction of Complex Dynamical …, 2021 - Springer
Matrix equations are omnipresent in (numerical) linear algebra and systems theory.
Especially in model order reduction (MOR), they play a key role in many balancing-based …

Low-complexity linear parameter-varying approximations of incompressible Navier-Stokes equations for truncated state-dependent Riccati feedback

J Heiland, SWR Werner - IEEE Control Systems Letters, 2023 - ieeexplore.ieee.org
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 …

Moment‐matching based model reduction for Navier–Stokes type quadratic‐bilinear descriptor systems

MI Ahmad, P Benner, P Goyal… - ZAMM‐Journal of …, 2017 - Wiley Online Library
We discuss a Krylov subspace projection method for model reduction of a special class of
quadratic‐bilinear descriptor systems. The goal is to extend the two‐sided moment …

Linear-quadratic optimal control of differential-algebraic systems: the infinite time horizon problem with zero terminal state

T Reis, M Voigt - SIAM Journal on Control and Optimization, 2019 - SIAM
In this work we revisit the linear-quadratic optimal control problem for differential-algebraic
systems on the infinite time horizon with zero terminal state. Based on the recently …

Example setups of Navier-Stokes equations with control and observation: Spatial discretization and representation via linear-quadratic matrix coefficients

M Behr, P Benner, J Heiland - arXiv preprint arXiv:1707.08711, 2017 - arxiv.org
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 …