Numerical Methods for Optimum Experimental Design
The aim of this research effort is to find out how model parameters in mathematical models for complex, time-dependent processes that can be described by means of differential equations, can be determined in a precise way with minimum experimental effort.
The mathematical formulation of the optimum experimental design task gives
a tricky nonlinear constrained optimization problem where a function of the
covariance matrix of a parameter estimation problem in DAE has to be
minimized. This corresponds to a maximization of the information gain in a statistical sense.
Design parameters include the discretized controls that
influence the respective dynamics, initial positions for the trajectories, and other control values.
Restrictions include geometrical constraints, path and control constraints, or experimental costs.
The resulting optimization problem is attacked with an SQP method
requiring one DAE model solution per iteration to resolve
cost functional and constraint values. In addition, second order
DAE solution derivatives with respect to the design variables
are needed to provide gradient information for the SQP method. These are
computed efficiently and accurately by solving the variational DAE.