Model Reduction and Control Design for Large-Scale Dynamical Systems

Mathematical models have proven to be indispensable tools to condense information, knowledge and understanding of complex physical systems. Especially for automatic and reliable control of processes, such models need to be accurate and computationally efficient, so as to allow fast predictions of changes in dynamical conditions. With modern computational tools it has become relatively easy to derive accurate mathematical models, but these models are invariably of large complexity and, in many applications, too slow to perform real time predictions that are suitable for control design. It is the purpose of this project to develop methodologies to infer simple substitute models for high-complexity (or large-scale) models that retain the accuracy of the original, complex model. The research activities will be particularly applied to large-scale numerical models that are inferred from nonlinear models of diffusive phenomena as they appear, e.g., in finite element models of glass furnaces. We aim for substantial reductions of model complexity, not possible with advanced meshing techniques, while control aims of the model are taken into account in an explicit manner.