Model reduction of port-hamiltonian systems

Promotie: dhr. R.V. Polyuga, 14.45 uur, Academiegebouw, Broerstraat 5, Groningen

Proefschrift: Model reduction of port-hamiltonian systems

Promotor(s): prof .dr. A.J. van der Schaft

Faculteit: Wiskunde en Natuurwetenschappen

Contact: Rostylav Polyuga, tel. 06-41107238, e-mail: rostyslav.polyuaga@gmail.com

Model reduction of port-hamiltonian systems

Port-based network modeling of physical systems leads directly to their representation as port-Hamiltonian systems. The port-Hamiltonian structure can be exploited for analysis and control. In particular, if the Hamiltonian function is non-negative then port-Hamiltonian systems are passive. At the same time network modeling of physical systems often leads to highdimensional dynamical models. Large state-space dimensions are obtained aswell if distributed parametermodels are spatially discretized. Therefore an important issue concerns the structure preserving model reduction of these high-dimensional systems, both for analysis and control. Within the systems and control literature there are several approaches for model reduction, which aimto approximate the external behavior of the high order system by low order models. On the other hand, these methods do not necessarily preserve structural properties of the system like passivity and the existence of conservation laws. This thesis offers a series of structure preserving model reduction methods for linear port-Hamiltonian systems. The resulting reduced order models retain the port-Hamiltonian structure, and, therefore, if the Hamiltonian function is non-negative, the properties of passivity and stability. Preservation of the port-Hamiltonian structure implies as well the ability to interconnect the reduced order models with other subsystems in complex networks, e.g. electrical circuits.