Proper orthogonal decomposition for constrained optimal control of PDEs
Abstract:
In this work optimal control problem for parabolic evolution problems
with inequality constraints are considered. For its numerical solution a
reduced-order approach based on proper orthogonal decomposition
(POD) is applied.
POD is a powerful technique for model reduction of non-linear dynamical
systems. It is based on a Galerkin type discretization with POD basis elements
created from the dynamical system itself.
In the talk the POD basis elements are computed from a reference trajectory
containing features which might be quite different from those of the optimally
controlled trajectory. Therefore, the error of the reduced-order solutions are
controlled by an a-posteriori error analysis. However, the POD approximation
may suffer from a badly chosen reference trajectory. Optimality system POD
(OS-POD) is utilized which avoids this problem.
The presented results are joint works with Carmen Gräßle, Eva Grimm, Martin
Gubisch, Karl Kunisch, Simone Metzdorf, Sabrina Rogg, Fredi Tröltzsch.
