New degrees of freedom and rigorous error bounds for the structure-preserving model order reduction of port-Hamiltonian systems

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The analysis, (control) design and optimization of dynamical systems with spatially distributed parameters is often based on high-dimensional discretized models, as they result e.g. from a finite element discretization of partial differential equations over a complex geometry. The amount of resulting ordinary differential equations is often very large (10.000 up to 1 million), hence making numerical computations unefficient. This motivates the use of model order reduction methods. Modelling of such systems in port-Hamiltonian (pH) form is particularly advantageous when the models result by thecoupling of subsystems, in which the physical variables describe the energy stored. Therefore, this model class will be the focus of this project. One goal is to preserve the characteristic pH-structure, to be taken advantage of in a subsequent control design or coupling. Convential reduction methods employ a relevant part of the availabledegrees of freedom for this structure preservation, providing less parameters to increase the approximation quality. The goal of this project is to introduce new degrees of freedom in the structure-preserving model order reduction of port-Hamiltonian systems andhence to extend existing results for general state-space models to this system class. Further, rigorous and global error bounds for the model reduction error are to be extended to the reduction of port-Hamiltonian systems.