Port-Hamiltonian systems represent an important and attractive novel paradigm for the mathematical modeling of dynamical systems. In contemporary research, the focus currently shifts from the analysis and treatment of closed systems to the interaction between multiple systems. In such networks of dynamical systems, the single constituents can be of very different nature, and it is the port-Hamiltonian paradigm with its distinguished emphasis on internal and external ports that allows for a universal mathematical description of the coupling between diverse systems while preserving crucial system properties. For example – and very importantly – port-Hamiltonian coupling genuinely guarantees stability of the overall system when the individual systems are stable, a feature that is lacking in other coupling approaches. The core of the port-Hamiltonian paradigm is a generalized concept of energy together with its flow along internal connections and external power-conjugate input and output ports. The conservation or dissipation properties of the modeling components as well as the identification of external ports play a central role. External ports allow, in particular, for a recursive coupling of mathematical models across different scales and domains. The generalized energy is encoded in the Hamiltonian, and the ports are defined by a Dirac structure. Together they provide the canonical framework for coupling and for the preservation of characteristic properties. Port-Hamiltonian systems currently evolve into an extremely powerful modeling tool for abstract dynamical systems leading to unprecedented progress in their mathematical analysis, their simulation and their optimization. To fully exploit the mathematical potential of port-Hamiltonian systems we thus need contributions from multiple mathematical disciplines. This interdisciplinary challenge is addressed by our CRC. We push the current limits in our understanding of port-Hamiltonian systems by focusing on analytical properties of infinite-dimensional systems, the preservation and usage of genuine structure-induced features in discretizations required for numerical simulation, and the exploitation of port-Hamiltonian structure in optimization, control and data-driven approaches. Advances in theory and methods are the main concern of our CRC. The inclusion of some specific applications ensures their practical relevance.
DFG Programme
Collaborative Research Centres
Current projects
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A01 - Infinite-dimensional port-Hamiltonian differential-algebraic systems
(Project Heads
Jacob, Birgit
;
Reis, Timo
)
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A02 - Port-Hamiltonian interacting particle systems: mean-field limit and control
(Project Heads
Jacob, Birgit
;
Totzeck, Claudia
)
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A03 - Structural analysis of infinite-dimensional port-Hamiltonian systems with resistive ports
(Project Heads
Glueck, Jochen
;
Jacob, Birgit
)
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A04 - Generalized passivity-based control of bilinear port-Hamiltonian systems
(Project Heads
Gernandt, Hannes
;
Reis, Timo
)
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A05 - Operator splitting for infinite-dimensional port-Hamiltonian systems
(Project Heads
Farkas, Balint
;
Jacob, Birgit
)
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B01 - Goal-oriented multirate and dynamic iteration methods for port-Hamiltonian differential-algebraic systems
(Project Heads
Bartel, Andreas
;
Schaller, Manuel
)
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B02 - Geometric numerical integration for port-Hamiltonian systems
(Project Heads
Günther, Michael
;
Marheineke, Nicole
)
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B03 - Stochastic port-Hamiltonian models for vehicle and pedestrian dynamics
(Project Heads
Rüdiger Mastandrea, Barbara
;
Tordeux, Antoine
)
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B04 - Linear solvers exploiting saddle point structure for port-Hamiltonian systems
(Project Heads
Bolten, Matthias
;
Ferrari, Paola
)
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B05 - Exploiting coupling and Dirac structure in numerical linear algebra kernels
(Project Heads
Frommer, Andreas
;
Kahl, Karsten
)
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B06 - Multi-coupled port-Hamiltonian models for electromagnetic problems
(Project Heads
Clemens, Markus
;
Günther, Michael
)
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C01 - Port-Hamiltonian methods in multi-objective shape optimization
(Project Heads
Bolten, Matthias
;
Gottschalk, Hanno
;
Klamroth, Kathrin
)
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C02 - Port-Hamiltonian Systems for dynamic nonlinear network flow problems
(Project Heads
Klamroth, Kathrin
;
Totzeck, Claudia
)
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C03 - Data-driven surrogate modelling for differential-algebraic port-Hamiltonian systems
(Project Heads
Günther, Michael
;
Zaspel, Peter
)
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C05 - Stochastic port-Hamiltonian systems and applications to stochastic optimal control
(Project Heads
Ehrhardt, Matthias
;
Kruse, Thomas
)
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C06 - Port-Hamiltonian methods for optimal control of large-scale systems
(Project Heads
Gernandt, Hannes
;
Schaller, Manuel
)
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MGK - Integrated Research Training Group
(Project Heads
Ehrhardt, Matthias
;
Frommer, Andreas
;
Glueck, Jochen
)
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S - Benchmark platform for port-Hamiltonian systems
(Project Heads
Gottschalk, Hanno
;
Zaspel, Peter
)
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Z - Central tasks of the Collaborative Research Centre
(Project Head
Jacob, Birgit
)
