Twenty years of distributed port-Hamiltonian systems: a literature review

Rashad, Ramy; Califano, Federico; Schaft, A.J. van der

doi:10.1093/imamci/dnaa018

Cited by 76 publications

(40 citation statements)

References 137 publications

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“…, and the relation: One can be confused by the lack of evolution in time in (5). However, this emphasizes an important paradigm in the proposed point of view: this relation translates the time-independent geometric structure of the pHs as an equation with differential operator (ill-posed on its own), while constitutive relations will bring back the time dependency of the problem.…”

Section: Structure Operatormentioning

confidence: 99%

“…[2] [3] [4]. This twenty-year-old framework [5] enjoys nice properties, such as the relevant physical meaning of the variables, a useful underlying linear structure (namely Stokes-Dirac structure) which encodes the power balance satisfied by the Hamiltonian (often chosen as energy), and last but not least: the interconnection of multiple pHs remains a pHs. This allows "modular" modelling of complex multiphysics systems.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, since they do not rely on well-established and versatile numerical libraries, using such techniques remains confined within a small community of experts. We refer the reader for a more complete overview of structure-preserving discretization for pHs to [5] [17] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Approximation of Port-Hamiltonian Systems for Hyperbolic or Parabolic PDEs with Boundary Control

Brugnoli¹,

Haine²,

Serhani³

et al. 2021

JAMP

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We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general structure of infinite-dimensional port-Hamiltonian systems (pHs) for which the Partitioned Finite Element Method (PFEM) straightforwardly applies. The proposed strategy is applied to abstract multidimensional linear hyperbolic and parabolic systems of PDEs. Then we show that instructional model problems based on the wave equation, Mindlin equation and heat equation fit within this unified framework. Secondly, we introduce the ongoing project SCRIMP (Simulation and Control of Interactions in Multi-Physics) developed for the numerical simulation of infinite-dimensional pHs. SCRIMP notably relies on the FEniCS open-source computing platform for the finite element spatial discretization. Finally, we illustrate how to solve the considered model problems within this framework by carefully explaining the methodology. As additional support, companion interactive Jupyter notebooks are available.

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Section: Structure Operatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Approximation of Port-Hamiltonian Systems for Hyperbolic or Parabolic PDEs with Boundary Control

Brugnoli¹,

Haine²,

Serhani³

et al. 2021

JAMP

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show abstract

“…In order to avoid unnecessary technicalities, the choice has been made to tackle the one-dimensional model, first derived in Section 2 as introductory example. Another fully worked out example can be found in Serhani et al (2019b) on the anisotropic heterogeneous wave equation in two-dimensional.…”

Section: Heterogeneous Case With Variable Coefficientsmentioning

confidence: 99%

“…The port-Hamiltonian formalism has proven to be a powerful tool for the modelling and control of complex multiphysics systems. In many cases, spatio-temporal dynamics must be considered and infinite-dimensional port-Hamiltonian models are needed (Rashad et al, 2020). Classical academic examples such as the transmission line, the shallow water or the beam equations have been investigated in the port-Hamiltonian framework (Duindam et al, 2009).…”

Section: Introductionmentioning

confidence: 99%

A partitioned finite element method for power-preserving discretization of open systems of conservation laws

Cardoso-Ribeiro

Matignon

Lefèvre

2020

IMA Journal of Mathematical Control and Information

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This paper presents a structure-preserving spatial discretization method for distributed parameter port-Hamiltonian systems. The class of considered systems are hyperbolic systems of two conservation laws in arbitrary spatial dimension and geometries. For these systems, a partitioned finite element method (PFEM) is derived, based on the integration by parts of one of the two conservation laws written in weak form. The non-linear one-dimensional shallow-water equation (SWE) is first considered as a motivation example. Then, the method is investigated on the example of the non-linear two-dimensional SWE. Complete derivation of the reduced finite-dimensional port-Hamiltonian system (pHs) is provided and numerical experiments are performed. Extensions to curvilinear (polar) coordinate systems, space-varying coefficients and higher-order pHs (Euler–Bernoulli beam equation) are provided.

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Soft sensor based on multi‐phase stacking ensemble model with self‐selected primary learner for batch processes

Zhao,

Yang,

et al. 2023

Can J Chem Eng

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In batch processes, existing soft sensing methodologies encounter substantial challenges when confronted with nonlinearity and multi‐phase issues. In response to these challenges, an innovative soft sensing framework known as the multi‐phase stacking ensemble model with self‐selected primary learner is proposed. The main innovation of this framework lies in the solution to the primary learner selection issue within the stacking model. To commence, the batch process is divided into multiple phases employing a Gaussian mixture model, thereby establishing local ensemble models for each phase. Subsequently, the iterative self‐selection of primary learners strategy is proposed, which iteratively selects suitable primary learners for these models, optimizing their combination of primary learners for each local model. This primary learner selection strategy effectively enhances the accuracy of predictions in the stacking ensemble model. To further enhance the performance, Bayesian optimization is utilized to tune the hyperparameters of each local ensemble model. This step guarantees optimal performance of the model across diverse phases. Extensive simulation experiments are conducted on an industrial penicillin fermentation process to validate the effectiveness of the proposed framework. According to the findings, the model demonstrated superior performance compared to existing single‐learner soft sensing methods and commonly utilized ensemble‐based soft sensing methods in terms of both R2 score (0.97584) and RMSE (0.0513). Overall, this framework offers a novel approach for selecting primary learners in stacking ensemble models and enhancing the predictive performance in batch processes for soft sensing.

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Twenty years of distributed port-Hamiltonian systems: a literature review

Cited by 76 publications

References 137 publications

Numerical Approximation of Port-Hamiltonian Systems for Hyperbolic or Parabolic PDEs with Boundary Control

Numerical Approximation of Port-Hamiltonian Systems for Hyperbolic or Parabolic PDEs with Boundary Control

A partitioned finite element method for power-preserving discretization of open systems of conservation laws

Soft sensor based on multi‐phase stacking ensemble model with self‐selected primary learner for batch processes

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