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- Peter Benner, Jan Heiland
- 2014

Recent theoretical and simulation results have shown that Riccati based feedback can stabilize flows at moderate Reynolds numbers. We extend this established control setup by the method of LQG-balanced truncation. In view of practical implementation, we introduce a controller that bases only on outputs rather than on the full state of the system. Also, weâ€¦ (More)

- JÃ¶rg Fehr, Jan Heiland, Christian Himpe, Jens Saak
- ArXiv
- 2016

Over the recent years the importance of numerical experiments has gradually been more recognized. Nonetheless, sufficient documentation of how computational results have been obtained is often not available. Especially in the scientific computing and applied mathematics domain this is crucial, since numerical experiments are usually employed to verify theâ€¦ (More)

We discuss the direct discretization of the input/output map of linear timeinvariant systems with distributed inputs and outputs. At first, the input and output signals are discretized in space and time, resulting in a matrix representation of an approximated input/output map. Then the system dynamics is approximated, in order to calculate the matrixâ€¦ (More)

- R. Altmann, Jan Heiland
- 2014

A general framework for the regularization of constrained PDEs, also called operator DAEs, is presented. The given procedure works for semi-explicit operator DAEs of first order which includes the Navier-Stokes and other flow equations. This reformulation is a regularization in the sense that a semi-discretization in space leads to a DAE of lower index,â€¦ (More)

- Jan Heiland
- 2012

We investigate existence and structure of solutions to quadratic control problems with semi-explicit differential algebraic constraints. By means of an equivalent index-1 formulation we identify conditions for the unique existence of optimal solutions. Knowing of the existence of an optimal input we provide a representation of the associated feedback-lawâ€¦ (More)

- R. Altmann, Jan Heiland
- 2015

We consider mechanical systems where the dynamics are partially constrained to prescribed trajectories. An example for such a system is a building crane with a load and the requirement that the load moves on a certain path. Modelling the system using Newtonâ€™s second law â€“ â€œThe force acting on an object is equal to the mass of that object times itsâ€¦ (More)

The construction of reduced order models for ow control via a direct discretization of the input/output behavior of the system is discussed. The spatially discretized equations are linearized such that an explicit formula for the corresponding input/output map can be used to generate a matrix representation of the input/output map. Estimates for theâ€¦ (More)

- Maximilian Behr, Peter Benner, Jan Heiland
- ArXiv
- 2017

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 package. We discuss the assembling of the system operators and the realization of boundary conditions and inputs and outputs. We describe the two benchmark problems driven cavityâ€¦ (More)

In the simulation of flows, the correct treatment of the pressure variable is the key to stable time-integration schemes. This paper contributes a new approach based on the theory of differential-algebraic equations. Motivated by the index reduction technique of minimal extension, a decomposition of finite element spaces is proposed that ensures stable andâ€¦ (More)

- Peter Benner, Jan Heiland
- 2017

Riccati-based feedback is commonly applied for the stabilization of flows in theory and in simulations. Nonetheless, there are few attempts to show the convergence of numerically computed feedback gains to the feedback defined by the actual model. In this work, we investigate how standard finite-dimensional formulations approximate the system dynamics andâ€¦ (More)