Numerical Solution of Optimal Control Problems with Instationary Diffusion-Convection and Diffusion-Reaction Equations
In this project we want to develop numerical algorithms of optimal control problems for instationary convection-diffusion and diffusion-reaction equations by using methods of state and output feedback. Linear problems with quadratic cost functional can be interpreted as a linear-quadratic regulator (LQR) problem. For the solutions of LQR problems new efficient methods were developed where Peter Benner was involved. These methods are coupled with solvers for the underlying stationary forward problem by appropriate interfaces. We obtain nonlinear problems if nonlinear differential operators or nonlinear boundary conditions occur. The solution of nonlinear problems can be found by solving a class of optimal control problems which are called tracking-problems by means of state or output feedback. Since in general the optimal control cannot be computed directly or with untenable effort as done in the linear case we will use sub-optimal strategies. We will focus on the development of numerical methods for the application of Model Predictive Control (MPC) for 2D and 3D problems. In doing so the whole time horizon will be covered by shorter time frames at which a sub-problem is solved by using an LQR or LQG design. The LQR and LQG designs for the parabolic problems arising after linearization can be solved by the numerical methods mentioned above.
Classification:
This is a successor of the sub-project A15 in DFG SFB393 Parallele Numerische Simulation für Physik und Kontinuumsmechanik
Related Talks:
Sabine Hein
MPC/LQG-basierte Optimalsteuerung für nichtlineare parabolische PDEs 14. Südostdeutsches Kolloquium zur Numerischen Mathematik;Universität Leipzig,
25. April 2008
Jens Saak
Efficient Implementation of Large Scale Lyapunov and Riccati Equation Solvers Computational Methods with applications 2007; Harrachov (Czech Republic);
20.-25. August 2007
Jens Saak
Application of LQR Techniques to the Adaptive Control of Quasilinear Parabolic PDEs ICIAM 2007; ETH Zürich;
16.-20 July 2007
Jens Saak
Numerische Verfahren zur optimalen Steuerung von parabolischen PDEs Workshop Mathematische Systemtheorie Elgersburg (Thüringen); Hotel am Wald Elgersburg;
18.-22. February 2007
Jens Saak
ADI shift parameter computation for large scale algebraic Riccati and Lyapunov equations arising in the LQR problem for parabolic PDEs ALA2006 Düsseldorf; Heinrich Heine University Düsseldorf
Düsseldorf, 23.-27. July 2006
Sabine Hein
MPC for the Burgers Equation Based on an LQG Design; GAMM Annual Meeting 2006; TU Berlin
Berlin, 27.-31. March 2006
Jens Saak
On Adi Parameters For Solving PDE Control-related Matrix Equations; GAMM Annual Meeting 2006; TU Berlin
Berlin, 27.-31. March 2006
Sabine Hein
Nonlinear Optimal Control Problems (Poster); German-Polish Workshop for Young Researchers in Applied and Numerical Linear Algebra; Mathematical Research and Conference Center
Bedlewo (Poland), 02.-04. February 2006
Jens Saak
Efficient numerical solution of large scale LQR problems arising in the optimal control of parabolic PDEs; German-Polish Workshop for Young Researchers in Applied and Numerical Linear Algebra; Mathematical Research and Conference Center
Bedlewo (Poland), 02.-04. February 2006