Optimal control-based feedback stabilization in multi-field flow problems

• Antragsteller: Professor Dr. Peter Benner; Professor Dr. Eberhard Bänsch
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2006 bis 2014
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 25165857

The goal in 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.

• DFG-Verfahren: Schwerpunktprogramme
• Teilprojekt zu: SPP 1253: Optimierung mit partiellen Differentialgleichungen