Jesper Carlsson
Department of Numerical Analysis
School of Computer Science and Communication
KTH, Stockholm
In this talk I will present a numerical method for approximation of some
optimal control problems for partial differential equations. Important
examples are inverse problems in optimal design, e.g. optimal material
design and parameter reconstruction. It is well known that inverse problems
often need to be regularized to obtain good approximations, however, there
is no complete theory how to regularize non-linear inverse problems. The
simple and general method I will present uses regularization, and error
estimates, derived from consistency with the corresponding
Hamilton-Jacobi-Bellman equations in infinite dimension.
If time allows, I will also discuss the inverse problem to find optimal
input data for parameter reconstruction problems. In this case the goal is
not just to recover an unknown parameter from measured data, but also to
find the optimal input from which measured data is generated, in order to
give a good reconstruction.