Stokes-Lagrange and Stokes-Dirac representations of $ N $-dimensional port-Hamiltonian systems for modeling and control
Year: 2025
Type: article
Abstract: In this paper, we extended the port-Hamiltonian framework by introducing the concept of Stokes-Lagrange structure, which enables the implicit definition of a Hamiltonian over an $ N $-dimensional domain and incorporates energy ports into the system. This new framework parallels the existing Dirac and Stokes-Dirac structures. We proposed the Stokes-Lagrange structure as a specific case where the subspace is explicitly defined via differential operators that satisfy an integration-by-parts formula. By examining various examples through the lens of the Stokes-Lagrange structure, we demonstrated the existence of multiple equivalent system representations. These representations provide significant advantages for both numerical simulation and control design, offering additional tools for the modeling and control of port-Hamiltonian systems.
DOI: 10.3934/cam.2025020
Authors: Antoine Bendimerad-Hohl, Fédération ENAC ISAE-SUPAERO ONERA, Université de Toulouse, Toulouse, France, Ghislain Haine, Laurent Lefèvre, Denis Matignon, Université Grenoble Alpes, Grenoble INP, Laboratoire de Conception et d'Intégration des Systèmes, Valence, France
Institutions: École Nationale de l’Aviation Civile, Institut Supérieur de l'Aéronautique et de l'Espace (ISAE-SUPAERO), Université de Toulouse, Institut polytechnique de Grenoble, Laboratoire de Conception et d'Intégration des Systèmes, Université Grenoble Alpes, Office National d'Études et de Recherches Aérospatiales
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4410265661