OATAO - Open Archive Toulouse Archive Ouverte Open Access Week

Anisotropic heterogeneous n-D heat equation with boundary control and observation : I. Modeling as port-Hamiltonian system

Serhani, Anass and Haine, Ghislain and Matignon, Denis Anisotropic heterogeneous n-D heat equation with boundary control and observation : I. Modeling as port-Hamiltonian system. (2019) In: 3rd IFAC Workshop on Thermodynamic Foundations for a Mathematical Systems Theory (TFMST 2019), 3 July 2019 - 5 July 2019 (Louvain-la-Neuve, Belgium).

[img]
Preview
(Document in English)

PDF (Author's version) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
365kB

Official URL: https://doi.org/10.1016/j.ifacol.2019.07.009

Abstract

The aim of this paper is to recast the heat equation with boundary control and observation in the port-Hamiltonian formalism. The anisotropic and heteregenous case in an n-D geometrical domain is systematically developped. Three different points of view are presented. The first two are thermodynamically founded, taking either entropy or energy as Hamiltonian functional. With the choice of entropy, the second principle can be recovered. With the choice of energy, following Zhou et al. (2017), extra physical variables are introduced allowing to recover the first principle. The third formulation is classical from a mathematical perspective, although less meaningful physically speaking; however the Hamiltonian proves to be a Lyapunov functional, which is useful for boundary control purposes. Moreover, all these three formulations can be discretized with a structure-preserving scheme, as presented in the companion paper Serhani et al. (2019a).

Item Type:Conference or Workshop Item (Paper)
HAL Id:hal-02279978
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Laboratory name:
Statistics:download
Deposited By: Ghislain Haine
Deposited On:05 Sep 2019 15:11

Repository Staff Only: item control page