INFIDHEM

Spring school "Theory and Applications of Port-Hamiltonian Systems"

HAINE Ghislain — 2018-04-09T10:19:49Z

31 March 2019 - 5 April 2019 in Munich, Gemany

Organized by Paul Kotyczka and Bernhard Maschke

- Spring school "Theory and Applications of Port-Hamiltonian Systems" / Gris

The Project

HAINE Ghislain — 2018-02-01T17:19:54Z

Motivated by recent technological progress in mechanical, aeronautical, energy systems and chemical engineering and novel computational tools, the analysis and control of infinite-dimensional systems became a field of major interest during the last decades. The basic concepts of classical systems theory have been progressively generalized to infinite-dimensional systems with contributions stemming from the mathematical as well as from the engineering community.

More recently, scientists became interested in understanding systems composed of distributed-parameter subsystems (described by systems of partial differential equations, PDEs) which interact in networks. Most of the existing literature on modeling, system analysis and control, deals with networks of homogeneous systems such as trusses of elastic rods or the heat conductivity properties of metal foams.

: Lab setup for heat conduction accessible to the Lyon partners

In this project, we shall consider networks of heterogeneous systems, which also involves transducers in the network to provide actuation, as for instance in smart foams for acoustics, or coupled mass and heat transport phenomena in catalytic foams. We will develop tools for their analysis, model reduction, simulation and control. The methodology used in this project, combines classical tools for infinite-dimensional systems and the theory of interconnected port-Hamiltonian (PH) systems.

A class of heterogeneous systems that we aim to study intensively are those describing fluid-structure-thermal interactions. The project aims to develop tools for the analysis and the control of these systems using control theoretic tools such as the theory of well-posed systems and its robustness with respect to nonlinear feedbacks in combination with passivity properties and the geometry of Hamiltonian systems.

Another important topic will be the development of model reduction techniques for such heterogeneous systems of PDEs by preserving some of their control theoretic properties or interconnection interfaces. The project aims at developing reduction methods for PH systems that preserve geometric structures, either Poisson bracket or Dirac structure. This may lead for instance in the case of systems of PDEs defined on graphs or more general k-complexes, to computational tools to obtain a reduced model defined on a clustered graphs or k-complexes with desired physical properties.

Finally the control of these heterogeneous systems of PDEs will be addressed by developing specific tools for instance for PH systems by designing the closed-loop using equivalence with PH systems with specified interconnection structure and physical (e.g. thermodynamic) properties. Moreover, the PH structure of the models, in finite and in infinite dimension, shall be used to develop adapted observers and computational methods for the trajectory planning. Test benches corresponding to the fields of expertise of the partners will serve as demonstrators.

: Topology of a metallic foam (extracted by image processing from tomography data)

: Airfoil flutter experiment in the Toulouse wind tunnel

Publications

HAINE Ghislain — 2017-03-03T12:11:18Z

Journal publications

Implying several partners

P. Kotyczka, B. Maschke, L. Lefèvre, Weak Form of Stokes-Dirac Structures and Geometric Discretization of Port-Hamiltonian Systems, J. of Computational Physics, Vol. 361, pp. 442-476, Mai 2018 DOI
Y. Wu, B. Hamroun, Y. Le Gorrec, B.Maschke, Reduced order LQG control design of port
Hamiltonian systems, Automatica, vol. 95, pp. 86-92, September 2018 DOI
V. Trenchant, H. Ramirez, Y. Le Gorrec, P. Kotyczka, Finite differences on taggered grids preserving the port-Hamiltonian structure with application to an acoustic duct, J. of Computational Physics, Vol. 373, pp.673-697, November 2018 DOI

Implying one partner

P. Kotyczka, Zur Erhaltung von Struktur und lecture Flachheit bei der torbasierten Ortsdiskretisierung (On the preservation of structure and flatness in port-based spatial discretization), at – Automatisierungstechnik, Vol. 66(7), pp. 521-535, 2018 DOI
S. Aouès, F. L. Cardoso-Ribeiro, D. Matignon, D. Alazard, Modeling and control of a rotating
flexible spacecraft: a port-Hamiltonian approach, IEEE Transactions on Control Systems Technology, 8 pages, 2018 DOI
E. Feireisl, V. Mácha, S. Necasova, M. Tucsnak, Analysis of the adiabatic piston problem via methods International of continuum mechanics, Annales de l'Institut Henri Poincaré C, Analyse non linéaire Vol. 35(5), pp. 1377-1408, August 2018 DOI

Conference publications

Implying several partners

P. Kotyczka, L. Lefèvre, Discrete-time port-Hamiltonian systems based on Gauss-Legendre collocation, 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, IFAC-PapersOnLine, Vol 51(3), pp. 125-130, 2018 DOI
F. L. Cardoso-Ribeiro, D. Matignon, L. Lefèvre, A structure-preserving Partitioned Finite Element Method for the 2D wave, 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, IFAC-PapersOnLine, Vol 51(3), pp. 119-124, 2018 DOI

Implying one partner

V. Trenchant, T. Vu, H. Ramirez, L. Lefèvre,Y. Le Gorrec, On the use of structural invariants for the distributed control of infinite dimensional port-Hamitonian systems, IEEE Conference on Decision and Control, Melbourne, Australia December 12-15, 2017
V. Trenchant, W. Hu, H. Ramirez, Y. Le Gorrec Structure preserving finite differences in polar coordinates for Heat and Wave equations, Mathmod, Vienna, Austria, February 21-23, 2018
Y. Wu, Y. Le Gorrec, Optimal actuator location for electro-active polymer actuated endoscope, 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, IFAC-PapersOnLine, Vol 51(3), pp. 199-204, 2018 DOI
P. Kotyczka, Structured discretization of the heat equation: Numerical properties and preservation of flatness, 23rd International Symposium on Mathematical Theory of Networks and Systems (MTNS2018), Hongkong, June 16-20, 2018
D. Alazard, S. Aoues, F. L. Cardoso-Ribeiro, DenisMatignon, Disturbance rejection for a rotating flexible spacecraft: a port-Hamiltonian approach, 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, IFAC-PapersOnLine, Vol 51(3), pp. 113-118, 2018 DOI
A. Serhani, D. Matignon, G. Haine, Structure-Preserving Finite Volume Method for 2D Linear and Non-Linear Port-Hamiltonian Systems, 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, IFAC-PapersOnLine, Vol 51(3), pp. 131-136, 2018 DOI
D. Matignon, Fractional Derivatives and Diffusive Representations: Semigroup formulation, Stability issues and Engineering Applications, Control of Distributed Parameter Systems
(CDPS 2017), Bordeaux, France, July 3-7, 2017
R. Muller, T. Hélie, Trajectory Anti-Aliasing on Guaranteed-Passive Simulation of Nonlinear Physical Systems, 20th International Conference on Digital Audio Effects (DAFx-17), Edinburgh, United Kingdom, September 5-9, 2017
M. Jossic, D. Roze, T. Hélie, B. Chomette, A. Mamou-Mani, Energy shaping of a softening Duffing oscillator using the formalism of Port-Hamiltonian Systems, 20th International Conference on Digital Audio Effects (DAFx-17), Edinburgh, United Kingdom, September 5-9, 2017
D. Roze, T. Hélie, Simulation passive d'un modèle réduit exact de plaque de Berger en grandes déformations, 14ème Congrès Français d'Acoustique, Le Havre, France, April 23-27, 2018
F. Silva, T. Hélie, Modélisation physique, simulation à bilan de puissance garanti et examen de régimes d'un appareil vocal simplifié, 14ème Congrès Français d'Acoustique, Le Havre, France, April 23-27, 2018

Private

HAINE Ghislain — 2017-03-03T12:09:06Z

To reach the private exchange folder of the project, follow the link NextCloud for INFIDHEM (access with the password you received on the mailing list).

Summer school "Control of Evolution Equations"

HAINE Ghislain — 2017-03-03T11:18:55Z

The school is on two topics of current interest in the field of systems and control theory of infinite-dimensional systems:

Marius Tucsnak (Bordeaux): Controllability of PDE systems at the crossing of functional and complex analysis with PDEs
Hans Zwart (Twente): Infinite-dimensional systems, state- and frequency domain techniques

For more informations: https://www.fan.uni-wuppertal.de/infidhemschool.html

Meetings

HAINE Ghislain — 2017-03-03T11:13:12Z

Kick-Off : the 03/01 and 03/02/2017 in LAGEP (Lyon).
The 10/05 and 10/06/2017 at Kiel University (Kiel)

The 04/05 and 04/06/2018 at ISAE (Toulouse)