### VPLAN

The scope of the VPLAN program package includes various mathematical methods for handling simulation and optimization tasks for multi-experiment systems with underlying DAE models. The following overview briefly describes the individual application modes:

- Integration: The DAE systems for the experiments of the experimental design are integrated. Output data are provided to visualize the trajectories. This mode assists the first phase of modeling before constraints and measurement procedures are specified.
- Simulation environment: In addition to integration, the measurement functions are evaluated. Covariance matrix, quality criteria and the approximations for the standard deviations of the parameters are calculated. The constraints on experimental design variables and state variables are checked for permissibility. If measured values are available, residuals are calculated, per measured value, per experiment and for the full multi experiment problem. The simulation environment thus provides a powerful tool for the simulation and evaluation of experimental designs. When used interactively, it provides an intuitive understanding of the model's behavior. By integrating the experiments, evaluating the measurement functions and adding up "noise", simulated measurement data can be generated.
- Parameter estimation: This mode allows solving multi-experiment parameter estimation problems by calling PARFIT or PAREMERA.
- Design of experiments: This is the central task of VPLAN. The experimental design variables of variable experiments are calculated in such a way that a quality criterion on the covariance matrix is optimized and the constraints are fulfilled. The calculation of the covariance matrix can include not only the experiments to be optimized but also fixed experiments that already have been carried out.

[1] Stefan Körkel, Numerische Methoden für Optimale Versuchsplanungsprobleme bei nichtlinearen DAE-Modellen (in German, English translation: Numerical Methods for Optimum Experimental Design with nonlinear DAE models), PhD Thesis, Heidelberg University, 2002. Online: http://archiv.ub.uni-heidelberg.de/volltextserver/2980/