Prof. Dr. Birgit Jacob
Prof. Dr. Michael Günther
Prof. Dr. Matthias Ehrhardt
|
Research Seminar Summer Term 2022:
Analysis and Numerics of port-Hamiltonian systems
Schedule
(Start of Seminar: May 3, 2022)
| Seminar |
Tuesday, 12:15 - 13:45 starting 03.05.2022 |
Room G.10.06 (Hörsaal 6) |
This is a seminar of the joint FAMNA group
Functional Analysis, Applied Mathematics and Numerical Analysis.
In this seminar we will discuss the port-Hamiltonian modelling approach for complex systems. Especially,
we will discuss topics like
port-based modeling of dynamic systems, Dirac structures, bond graph notation, 0- and 1-junctions, computational causality,
causal analysis, hierarchical modeling, port concept, well-posedness of port-Hamiltonian systems,
passivity, infinite-dimensional port-Hamiltonian systems, Control of Finite-Dimensional Port-Hamiltonian Systems,
discrete-time port-Hamiltonian systems, stochastic port-Hamiltonian Systems.
The seminar is suitable for Master and PhD students of mathematics, economathematics, technomathematics, physics.
Schedule of the Seminar:
- May 3, 2022: Birgit Jacob, Einführung in port-Hamiltonsche Systeme
- May 10, 2022: Birgit Jacob, Einführung in port-Hamiltonsche Systeme II
- May 17, 2022: Birgit Jacob, Einführung in port-Hamiltonsche Systeme III
- May 24, 2022: Michael Günther, Symplektische Integratoren I
- May 31, 2022: Michael Günther, Symplektische Integratoren II
- June 14, 2022: no talk
- June 27, 2022: Benjamin Unger (U Stuttgart), Towards optimal surrogates for port-Hamiltonian systems - energy functionals
and system norms, 16:00st, Room FZ.02.06, Lise-Meitner-Str. 27-31.
- June 28, 2022: Björn Liljegren Sailer (U Trier), Port-Hamiltonsche Diskretisierung und Modellreduktion,
11:30st, Room FME 01.04, 1st floor, Rainer-Gruenter-Str. 21.
- June 28, 2022: Andrea Brugnoli (U Twente), Improving multiphysics simulation through port-Hamiltonian system theory,
14:00st, Room FME 01.04, 1st floor, Rainer-Gruenter-Str. 21.
- June 29, 2022: Nathanael Skrepek (Bergakademie Freiberg), Semi-uniform stability of Maxwell's equations,
11:30st, FZ.00.23, Lise-Meitner-Str. 27-31.
- June 29, 2022: Hannes Gernandt (TU Berlin), Perspectives in port-Hamiltonian modelling of energy systems,
14:00st FZ.00.23, Lise-Meitner-Str. 27-31.
- July 6, 2022: Karim Cherifi (TU Berlin), Data-driven port-Hamiltonian modeling as enabler for digital twins,
17:00st FZ.00.23, Lise-Meitner-Str. 27-31.
Literature:
- A. van der Schaft,
Port-Hamiltonian systems: an Introductory Survey,
in: M. Sanz-Sole, J. Soria, J.L. Varona, J. Verdera (eds.),
Proceedings of the International Congress of Mathematicians Vol. III,
Madrid, Spain, 2006, pp. 1339-1365.
- B. Jacob, H. Zwart,
Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces,
Springer 2012.
- C. Beattie, V. Mehrmann, H. Xu, H. Zwart,
Linear Port-Hamiltonian Descriptor Systems,
Math. Control Signals Syst. (December 2018) 30: 17.
- V. Duindam, A. Macchelli, S. Stramigioli, H. Bruyninckx (eds.),
Modeling and Control of Complex Physical Systems - The Port-Hamiltonian Approach,
Springer 2009.
- P. Kotyczka, L. Lefèvre,
Discrete-time port-Hamiltonian systems: A definition based on symplectic integration,
arXiv:1811.07852 [math.DS] (Nov 2018).
- M. Maciejewski,
Co-Simulation of Transient Effects in Superconducting Accelerator Magnets,
Dissertation, Lódź, October 2018.
- A. van der Schaft, D. Jeltsema,
Port-Hamiltonian Systems Theory: An Introductory Overview,
Foundations and Trends in Systems and Control 1(2-3) (2014), 173-378.
- M. Šešlija,
Discrete geometry approach to structure-preserving discretization of Port-Hamiltonian systems,
Dissertation, University of Groningen, 2013.
The topics are intended to be dealt with:
Analysis of PHS
- H. Ramírez, Y. Le Gorrec, A. Macchelli, H. Zwart,
Exponential stabilization of boundary controlled port-Hamiltonian systems with dynamic feedback,
IEEE Trans. Automat. Control 59(10) (2014), 2849-2855.
- H. Ramírez, H. Zwart, Y. Le Gorrec,
Stabilization of infinite dimensional port-Hamiltonian systems by nonlinear dynamic boundary control,
Automatica J. IFAC 85 (2017), 61-69.
- J.-P. Humaloja, L. Paunonen,
Robust regulation of infinite-dimensional port-Hamiltonian systems,
IEEE Trans. Automat. Control 63(5) (2018), 1480-1486.
- B. Augner, B. Jacob,
Stability and stabilization of infinite-dimensional linear port-Hamiltonian systems,
Evol. Equ. Control Theory 3(2) (2014), 207-229.
Structure Preserving MOR
- S. Chaturantabut, C. Beattie, S. Gugercin,
Structure-Preserving Model Reduction for Nonlinear Port-Hamiltonian Systems,
SIAM J. Sci. Comput. 38(5), B837-B865.
- R.V. Polyuga, A. van der Schaft,
Effort- and flow-constraint reduction methods for structure preserving model reduction of port-Hamiltonian systems,
Systems & Control Letters 61(3) (2012), 412-421.
- C. Beattie, S. Gugercin,
Structure-preserving model reduction for nonlinear port-Hamiltonian systems,
50th IEEE Conference on Decision and Control and European Control Conference, 2011.
- R.V. Polyuga, A. van der Schaft,
Structure preserving model reduction of port-Hamiltonian systems by moment matching at infinity,
Automatica 46(4) (2010), 665-672.
- T. Wolf, B. Lohmann, R. Eid, P. Kotyczka,
Passivity and Structure Preserving Order Reduction of Linear Port-Hamiltonian Systems Using Krylov Subspaces,
European Journal of Control 4 (2010), 401-406.
- A. Yaghmaei, M.J.Yazdanpanah,
Structure Preserving Observer Design for Port-Hamiltonian Systems,
IEEE Transactions on Automatic Control 2018.
- R.V. Polyuga, A. van der Schaft,
Structure Preserving Port-Hamiltonian Model Reduction of Electrical Circuits,
in: P. Benner, M. Hinze, E. ter Maten (eds.),
Model Reduction for Circuit Simulation,
Lecture Notes in Electrical Engineering 74, Springer, 2011, pp. 241-260.
- B. Lohmann, T. Wolf, R. Eid, P. Kotyczka,
Passivity Preserving Order Reduction of Linear Port-Hamiltonian Systems by Moment Matching,
Technical Reports on Automatic Control Vol. TRAC-4, August 2009.
- K. Fujimoto,
Balanced Realization and Model Order Reduction for Port-Hamiltonian Systems,
Journal of System Design and Dynamics 2(3) (2008), 694-702.
Stochastic Port-Hamiltonian Systems
- F. Lamoline, J.J. Winkin,
On Stochastic port-Hamiltonian Systems with Boundary Control and Observation,
2017 IEEE 56th Annual Conference on Decision and Control (CDC)
December 12-15, 2017, Melbourne, Australia, pp. 2492-2497.
- F. Lamoline, J.J. Winkin,
On LQG control of stochastic port-Hamiltonian systems on infinite-dimensional spaces,
23rd International Symposium on Mathematical Theory of Networks and Systems
Hong Kong University of Science and Technology, Hong Kong, July 16-20, 2018, pp. 197-203.
- S. Satoh, K. Fujimoto,
Passivity Based Control of Stochastic Port-Hamiltonian Systems,
IEEE Transactions on Automatic Control 58(5), 2013.
- Z. Fang, C. Gao,
Stabilization of Input-Disturbed Stochastic Port-Hamiltonian Systems Via Passivity,
IEEE Transactions on Automatic Control 62(8), 2017.
- P. Jagtap, M. Zamani,
Backstepping Design for Incremental Stability of Stochastic Hamiltonian Systems with Jumps,
IEEE Transactions on Automatic Control 63(1), 2018.
- J.-Y. Li, Y.-H. Liu, S.-X. Tang, X.-S. Cai,
Observer-based Stabilization of Stochastic Hamiltonian Systems,
2018 Annual American Control Conference (ACC),
June 27-29, 2018. Wisconsin Center, Milwaukee, USA, pp. 5940-5945.
- Y. Sun, J. Zhao,
Passivity-based Stabilization for Switched Stochastic Nonlinear Systems,
IEEE/CAA Journal of Automatica Sinica, 2018.
Discretization of PHS
- P. Kotyczka, B. Maschke, L. Lefèvre,
Weak form of Stokes-Dirac structures and geometric discretization of port-Hamiltonian systems,
Journal of Computational Physics 361 (2018), 442-476.
- A. Serhani, D. Matignon, G. Haine,
Structure-Preserving Finite Volume Method for 2D Linear and Non-Linear Port-Hamiltonian Systems,
In: 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control,
1 May 2018 - 4 May 2018 (Valparaíso, Chile).
- V. Trenchant, W. Hu, H. Ramirez, Y. Le Gorrec,
Structure Preserving Finite Differences in Polar Coordinates for Heat and Wave Equations,
IFAC-PapersOnLine 51(2) (2018), 571-576.
- V. Talasila, J. Clemente-Gallardo, A. J. van der Schaft,
Discrete port-Hamiltonian systems,
Systems & Control Letters 55 (6) (2006) 478-486.
- V. Talasila, J. Clemente-Gallardo, A. J. van der Schaft,
Discrete port-Hamiltonian systems,
IFAC Proceedings Volumes 38(1) (2005), 495-500.
- E. Celledoni, E.H. Høiseth,
Energy-preserving and passivity-consistent numerical discretization of port-Hamiltonian systems,
arXiv preprint arXiv:1706.08621.
- P. Kotyczka, L. Lefèvre,
Discrete-time port-Hamiltonian systems based on Gauss-Legendre collocation,
IFAC-PapersOnLine 51(3) (2018), 125-130.
- S. Aoues, D. Eberard, W. Marquis-Favre,
Canonical interconnection of discrete linear port-Hamiltonian systems,
in: 52nd IEEE Conference on Decision and Control, IEEE, 2013, pp. 3166-3171.
- P. Kotyczka,
Zur Erhaltung von Struktur und Flachheit bei der torbasierten Ortsdiskretisierung
(On the preservation of structure and flatness in port-based spatial discretization),
- L. Gören-Sümer, Y. Yalcin,
Gradient based discrete-time modeling and control of Hamiltonian systems,
IFAC Proceedings Volumes 41 (2) (2008) 212-217.
Modelling
- S. Fiaz, D. Zonetti, R. Ortega, J.M. Scherpen, A. van der Schaft,
A port-Hamiltonian approach to power network modeling and analysis,
Eur. J. Control 19(6) (2013), 477-485.
- V. Mehrmann, R. Morandin, S. Olmi, E. Schöll,
Qualitative Stability and Synchronicity Analysis of Power Network Models in Port-Hamiltonian Form,
arXiv:1712.03160 [cond-mat.dis-nn] (2017).
- D. Sbarbaro,
On the Port-Hamiltonian Models of some Electrochemical Processes,
IFAC-PapersOnLine 51(3) (2018), 38-43.
- F. Strehle, M. Pfeifer, L. Kölsch, C. Degünther, J. Ruf, L. Andresen, S. Hohmann,
Towards Port-Hamiltonian Modeling of Multi-Carrier Energy Systems:
A Case Study for a Coupled Electricity and Gas Distribution System,
IFAC-PapersOnLine 51(2) (2018), 463-468.
- B. Vincent, T. Vu, N. Hudon, L. Lefèvre, D. Dochain,
Port-Hamiltonian modeling and reduction of a burning plasma system,
IFAC-PapersOnLine 51(3) (2018), 68-73.
- D. Zonetti, B. Yi, S. Aranovskiy, D. Efimov, R. Ortega, E. Garìa-Quismondo,
On Physical Modeling of Lithium-Ion Cells and Adaptive Estimation of their State-of-Charge,
In: 57th IEEE Conference on Decision and Control (CDC 2018),
Fontainebleau in Miami Beach, FL, US, 2018.
Application to Electrodynamics
- A.J. van der Schaft, B.M. Maschke,
Hamiltonian formulation of distributed-parameter systems with boundary energy flow,
Journal of Geometry and Physics 42(1-2) (2002), 166-194.
- O. Farle, D. Klis, M. Jochum, O. Floch, R. Dyczij-Edlinger,
A port-Hamiltonian finite-element formulation for the Maxwell equations,
International Conference on Electromagnetics in Advanced Applications (ICEAA), 2013, pp. 324-327.
- D. Jeltsema A. van der Schaft,
Pseudo-gradient and Lagrangian boundary control system formulation of electromagnetic fields,
J. Phys. A: Math. Theor. 40 (2007), 11627.
- E. Garcí-Canseco, R. Ortega, J.M. Scherpen, D. Jeltsema,
Power Shaping Control of Nonlinear Systems: A Benchmark Example,
in: F. Allgüwer et al. (eds.),
Lagrangian and Hamiltonian Methods for Nonlinear Control 2006,
Lecture Notes in Control and Information Sciences 366, Springer, 2007, pp. 135-146.
- R.S. Ingarden, A. Jamiolkowski,
Classical Electrodynamics, Elsevier, 1985.
Other
- A. van der Schaft, B. Maschke,
The Hamiltonian formulation of energy conserving physical systems with external ports,
Archiv für Elektronik und Übertragungstechnik 49(5/6) (1995), 362-371.
- T. Voss,
Port-Hamiltonian modeling and control of piezoelectric beams and plates:
application to inflatable space structures,
Dissertation, Groningen, 2010.
- M. Šešlija, A. van der Schaft, J.M.A.Scherpen
Discrete exterior geometry approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems,
Journal of Geometry and Physics 62(6) (2012), 1509-1531.
- A. van der Schaft, B. Maschke,
Generalized Port-Hamiltonian DAE Systems,
arXiv:1808.01845 [math.OC] 2018.
- A. Brugnoli, D. Alazard, V. Pommier-Budinger,
Port-Hamiltonian formulation and Symplectic discretization of Plate models. Part I: Mindlin model for thick plates,
arXiv:1809.11131 [math.AP] 2018.
- A. Brugnoli, D. Alazard, V. Pommier-Budinger, D. Matignon,
Port-Hamiltonian formulation and Symplectic discretization of plate models. Part II : Kirchhoff model for thin plates,
arXiv:1809.11136 [math.AP] September 2018.
- M. Šešlija, J.M.A.Scherpen, A. van der Schaft,
Port-Hamiltonian systems on discrete manifolds,
IFAC Proceedings Volumes 45(2) (2012), 774-779.
- G. Golo, A. van der Schaft, P.C. Breedveld, B.M. Maschke,
Hamiltonian formulation of bond graphs, 2003.
- P. Gawthrop, E.J. Crampin,
Bond Graph Representation of Chemical Reaction Networks,
IEEE Transactions on Nanobioscience 17(4) (2018), 449-455.
- R.V. Meshram, S.V. Khade, S.R. Wagh, N.M. Singh, A.M. Stanković,
Bond graph approach for port-controlled Hamiltonian modeling for SST,
Electric Power Systems Research 158, (2018), 105-114
Criteria for successfully passing the course:
Presentation
Written draft paper (approx. 10 pages, incl. examples)
Regular participation in the seminar
Previous knowledge:
Analysis I - III, basic knowledge of ordinary differential equations and numerical mathematics.
