2020
DOI: 10.1093/imamci/dnaa018
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Twenty years of distributed port-Hamiltonian systems: a literature review

Abstract: The port-Hamiltonian (pH) theory for distributed parameter systems has developed greatly in the past two decades. The theory has been successfully extended from finite-dimensional to infinite-dimensional systems through a lot of research efforts. This article collects the different research studies carried out for distributed pH systems. We classify over a hundred and fifty studies based on different research focuses ranging from modeling, discretization, control and theoretical foundations. This literature re… Show more

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Cited by 91 publications
(40 citation statements)
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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%
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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%
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“…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%