Software presented at the workshop “Quantitative Local Analysis of Nonlinear Systems Using Sum-of-Squares Decompositions” on June 9, 2009 at the American Controls Conference in St. Louis, Missouri.
The Data Collaboration MATLAB toolbox is a software package designed to integrate experimental data into quantitative predictive models. In the academic environment, the methodology facilitated by the software has been applied to a combustion chemistry application and an atmospheric chemistry application. The software allows the user to input results of one or more experimental measurements taken on the system along with their expected uncertainty. Taken with a parametrized model, the observations implicitly describe a set of feasible parameter values. Questions about this set, such as is it nonempty (model validation) or what is the range of values a given model can take over it (model prediction) are posed as mathematical programs. These are solved by recently developed techniques for optimization problems involving polynomials.