## 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 non-standard nonlinear constrained optimization problem where a function of the covariance matrix (describing the uncertainty) 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 tackled 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 or using algorithmic differentiation combined with internal numerical differentiation.

Software Package:

VPLAN