Control of Partial Differential Equations: A port-Hamiltonian approach
Final Report Abstract
This project was conducted as part of the NWO-DFG Bilateral Cooperation programme with Prof. Zwart (University of Twente). Supported by this grant, a workshop on Port-Hamiltonian systems: Approximation, Theory and Practice at the Lorentz center in Leiden and a summer school on Modeling and Control of Distributed Parameter Systems at the University of Twente were organized. Morever, several research stay could be realized. Hamiltonian dynamics is a well-known topic within mathematics and physics. Combining this concept with concepts from system and control theory has led to the port-Hamiltonian system class. For systems described by ordinary differential equations this approach is wellstudied and has resulted in new control strategies. For systems described by partial differential equations there are several promising approaches, but the theory is much less mature than for ordinary differential equations. In this project we brought together experts working in the field of port-Hamiltonian systems and its neighboring fields. This lead to more insight in the analysis and controller design for this systems class. More precisely, we studied approximation of port-Hamiltonian systems, system theoretical properties and non-linear port-Hamiltonian systems. Significant results concerning system theoretical properties of infinite-dimensional systems and in particular port-Hamiltonian systems, such as the root locii and well-posedness, were proved. The obtained results are already published in international journals.
Publications
- C0-semigroups for hyperbolic partial differential equations on a one-dimensional spatial domain, Journal of Evolution Equations, 15(2) (2015), 493-502
Birgit Jacob, Kirsten Morris and Hans Zwart
(See online at https://doi.org/10.1007/s00028-014-0271-1) - Root locii for systems defined on Hilbert spaces. In: IEEE Transaction on Automatic Control, Volume: 61 , Issue: 1 , Jan. 2016, 116-128
Birgit Jacob and Kirsten Morris
(See online at https://doi.org/10.1109/TAC.2015.2433991)
