Discrete-time port-Hamiltonian systems: A definition based on symplectic integration

We introduce a new definition of discrete-time port-Hamiltonian systems (PHS), which results from structure-preserving discretization of explicit PHS in time. We discretize the underlying continuous-time Dirac structure with the collocation method and add discrete-time dynamics by the use of symplectic numerical integration schemes. The conservation of a discrete-time energy balance - expressed in terms of the discrete-time Dirac structure - extends the notion of symplecticity of geometric integration schemes to open systems. We discuss the energy approximation errors in the context of the presented definition and show that their order is consistent with the order of the numerical integration scheme. Implicit Gauss-Legendre methods and Lobatto IIIA/IIIB pairs for partitioned systems are examples for integration schemes that are covered by our definition. The statements on the numerical energy errors are illustrated by elementary numerical experiments.Comment: 12 pages. Preprint submitted to Systems & Control Letter

Weak Form of Stokes-Dirac Structures and Geometric Discretization of Port-Hamiltonian Systems

We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure with a segmented boundary according to the causality of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac structure by a finite-dimensional Dirac structure is realized using a mixed Galerkin approach and power-preserving linear maps, which define minimal discrete power variables. (iii) With a consistent approximation of the Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models. By the degrees of freedom in the power-preserving maps, the resulting family of structure-preserving schemes allows for trade-offs between centered approximations and upwinding. We illustrate the method on the example of Whitney finite elements on a 2D simplicial triangulation and compare the eigenvalue approximation in 1D with a related approach.Comment: Copyright 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0

Discrete-time port-Hamiltonian systems: A definition based on symplectic integration

International audienceWe introduce a new definition of discrete-time port-Hamiltonian systems (PHS), which results from structure-preserving discretization of explicit PHS in time. We discretize the underlying continuous-time Dirac structure with the collocation method and add discrete-time dynamics by the use of symplectic numerical integration schemes. The conservation of a discrete-time energy balance-expressed in terms of the discrete-time Dirac structure-extends the notion of symplecticity of geometric integration schemes to open systems. We discuss the energy approximation errors in the context of the presented definition and show that their order is consistent with the order of the numerical integration scheme. Implicit Gauss-Legendre methods and Lobatto IIIA/IIIB pairs for partitioned systems are examples for integration schemes that are covered by our definition. The statements on the numerical energy errors are illustrated by elementary numerical experiments

Mieszkając ze zwierzętami : domowa koegzystencja ludzi i zwierząt w perspektywie posthumanizmu

The dissertation’s aim is to present the relationships between humans and animals that form and evolve in home. Using the view of posthumanism allowed to address such issues as interspecies affections, modes of representation of the animal, food taboos, the differences between the biological systematics and volk taxonomy, redefinition of language. The construction of the definition of pets and companion animals was an important part of the work, as well as the discussion about the posthuman optics. The dissertation contains a theoretical part, four analytical parts and summary. Sequence of the analysis sections corresponds to the chronology of the relationships between human and animal, and presents itself as follows: Zoonatologies present the birth of the companion species, namely the creation of pets for man and man for pets. I made reinterpretation of the major myths standing at the beginning of the human-animal relation, I presented the places, where human and animal meet, and I analyzed their semiotics. An important element was to discuss the problem of love as affection, which can constitute the existence of the categories of pets and companion animals. Zoadolescence is about the adolescence of the human relationship with pets. I discussed the basics of the animal rights that refer to pets, as well as the food taboos and shame as an influence on human-animal relationship. Zooptics show how looking at animals confuses the ontological and epistemological questions. The main goal of the four sections was to revise the concept of animal gaze, extremely popular in animal studies in recent years. Zoonekrographies are an attempt to restore the death of the animal. I discussed in this part the philosophical voices about the difference between the death of the human and the death of the animal. I analyzed the function of pet cemeteries, and I introduced the myth of the return of the animal, which, in various forms, reflects the condition of the human-animal relationship. The study analyzed a variety of sources: literature, video, tv shows, advertising and graphic. The taken analysis were mostly inspired by thinkers such as Jacques Derrida, Bruno Latour, Cary Wolfe, Donna Haraway, Erica Fudge, Yi-Fu Tuan, Sarah Ahmed

Kobiety, psy i koty : domowa koegzystencja ludzi i zwierząt w literaturze familijnej

The article discusses the issue of living and thinking with pets. The author analyzes examples of popular literature, particularly books addressed to families and women, in order to seek for animal agency in the plot. The thesis is based on an assumption about the special bond between pets and female characters in such novels. Verifying the theory of Yi-Fu Tuan from his book Dominance and Affection. Making of Pets, the article questions pets as an effect of the human tendency to domination over nature and taking comfort in a coherent view of animals. Pets, according to Tuan’s theory, ought to be reflections of human desires and needs. The domination in its roots is male, but its repressive demands involve pets as well as women. This is the premise whereby the special relation between pets and female owners has evolved. That is the reason why it is important to examine the meaning of human-animal relations by considering gender. The space where the bond between women and their pets starts and develops is also significant. The home is the third main character of each novel, and maintains an actually dynamic relation with others

Port-Hamiltonian formulation and structure-preserving discretization of hyperelastic strings

Port-Hamiltonian (PH) systems provide a framework for modeling, analysis and control of complex dynamical systems, where the complexity might result from multi-physical couplings, non-trivial domains and diverse nonlinearities. A major benefit of the PH representation is the explicit formulation of power interfaces, so-called ports, which allow for a power-preserving interconnection of subsystems to compose flexible multibody systems in a modular way. In this work, we present a PH representation of geometrically exact strings with nonlinear material behaviour. Furthermore, using structure-preserving discretization techniques a corresponding finite-dimensional PH state space model is developed. Applying mixed finite elements, the semi-discrete model retains the PH structure and the ports (pairs of velocities and forces) on the discrete level. Moreover, discrete derivatives are used in order to obtain an energy-consistent time-stepping method. The numerical properties of the newly devised model are investigated in a representative example. The developed PH state space model can be used for structure-preserving simulation and model order reduction as well as feedforward and feedback control design.Comment: Submitted as a proceeding to the ECCOMAS Thematic Conference on Multibody Dynamics 202

Box spline prewavelets of small support

The purpose of this paper is the construction of bi- and trivariate prewavelets from box-spline spaces, \ie\ piecewise polynomials of fixed degree on a uniform mesh. They have especially small support and form Riesz bases of the wavelet spaces, so they are stable. In particular, the supports achieved are smaller than those of the prewavelets due to Riemenschneider and Shen in a recent, similar constructio

Partitioned finite element method for structured discretization with mixed boundary conditions

The propagation of acoustic waves in a 2D geometrical domain under mixed boundary control is here described by means of the port-Hamiltonian (pH) formalism. A finite element based method is employed to obtain a consistently discretized model. To construct a model with mixed boundary control, two different methodologies are detailed: one employs Lagrange multipliers, the other relies on a virtual domain decomposition to interconnect models with different causalities. The two approaches are assessed numerically, by comparing the Hamiltonian and the state variables norm for progressively refined meshes