joint work with Hans Georg Bock, Kathrin Hatz, Ekaterina Kostina, Katja Mombaur, Johannes P. Schlöder, Sebastian Wolf
Inverse optimal control problems arise in the field of modeling, simulation and optimization of the human gait. For our studies we consider a bilevel optimization problem. The lower optimal control model includes unknown parameters that have to be determined by fitting the model to measurements, which is done in the upper level. We present mathematical and numerical methods using a simultaneous direct approach for inverse optimal control problems and derive optimal control models for the gait of patients with cerebral palsy from real-world motion capture data.
joint work with Andreas Sommer, Hans Georg Bock, Ekaterina Kostina, Johannes P. Schlöder
For ODEs with switched or non-smooth dynamics, modelers often provide code containing conditionals like IF, ABS, MIN, and MAX. Standard black-box integrators, in general, show poor performance or may compute wrong dynamics without notice. Transformation into model descriptions suitable for state-of-the-art methods is often cumbersome or infeasible. In this talk, we present a new approach that works on the dynamic model equations as provided by the modeler and allows to treat switched and non-smooth large-scale dynamics efficiently and accurately for both integration and sensitivity generation.
joint work with Lorenz Biegler, Lu Han, Jason Mustakis
The development of drug manufacturing processes involves dealing with spectroscopic data. In many cases kinetic parameter estimation from spectra has to be performed without knowing the absorbing species in advance, such that they have to be estimated as well. That is why we take a closer look at the development of optimization-based procedures in order to estimate the variances of system and measurement noise and thus determine the concentration and absorbance profiles, and parameters simultaneously. The further investigations related to the application specific challenges are presented.