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Computational Methods in Systems and Control Theory

OptConFee- StabMultiFlow


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DFG Priority Program 1253: Optimization With Partial Differential Equations

Project

Optimal Control-Based Feedback Stabilization of Multi-Field Flow Problems


The goal of this project is to derive and investigate numerical algorithms for optimal control-based boundary feedback stabilization of multi-field flow problems.

We will follow an approach laid out during the last years in a series of papers by Barbu, Lasiecka, Triggiani, Raymond, and others. They have shown that it is possible to stabilize perturbed flows described by the Navier-Stokes equation by designing a stabilizing controller based on a corresponding linear-quadratic optimal control problem.

Until recently, the numerical solution of these linear-quadratic optimal control problem was a numerical challenge due to the complexity of existing algorithms. Employing recent advances in reducing these complexities essentially to a cost proportional to the simulation of the forward problem, we plan to apply this methodology to multi-field problems where the flow is coupled with other field equations.

We suggest three scenarios with increasing difficulty for which we want to demonstrate the applicability of the optimal control-based feedback stabilization approach.

The scenarios are the following:

Principal investigators:

Prof. Dr. Peter Benner
Prof. Dr. Eberhard Bänsch
(Applied Mathematics III, FAU Erlangen)

Researcher:

Anne Katrin Heubner (11/2006-09/2008)
Dr. Jens Saak (10/2009-01/2011)
Heiko Weichelt (since 06/2011)

Student Assistants:

Martin Köhler (05/09-10/10)
Heiko Weichelt (11/08-12/10)

Simulations:

Navier-Stokes on von Kármán vortex street

Example: Re=500, t_end=30
Control input over boundary after t_control=10

Openloop control with constant input

Download as AVI in higher quality (ca. 12 MB)

(Non optimal) feedback

Download as AVI in higher quality (ca. 19 MB)

Goal: Get laminar flow behind the obstacle.

Navier-Stokes coupled with transport of some species

Example: Re=10, Sc=10, t_end=60 (left picture)
Piecewise constant control input (right picture)

3D-Simulation of concentration

Download as AVI in higher quality (ca. 60 MB)

2D-Simulation of concentration
Download as AVI in higher quality (ca. 80 MB)

Goal: Get a fixed rate of reaction on the obstacle.

Navier-Stokes on von Kármán vortex street


Example: Re=300, t_end=40

Feedback stabilization over boundary influence after t_control=7.5 for initial and optimal feedback.
Download as AVI in higher quality (ca. 69 MB)

Goal: Vanish y-components of flow in grid fields 3 and 4 of the 3rd row.

Publications:

Related Posters:

Reports:

Talks and Presentations:


©2018, Max Planck Society, Munich
Heiko Weichelt, heiko.weichelt@mathematik.tu-chemnitz.de
25 Januar 2016