Structure-preserving discretization of multidimensional linear port-Hamiltonian systems using FEM approaches

Authors

Cristobal Ponce, Yongxin Wu, Yann Le Gorrec, Hector Ramirez

Abstract

This study introduces a novel control oriented structure-preserving scheme for discretizing a class of multi-dimensional linear port-Hamiltonian systems, preserving their inherent structure while enabling the imposition of diverse combinations of boundary inputs, such as generalized velocities, displacements, and tractions. The proposed approach is grounded on the modified Linked Lagrange Multiplier method and the mixed Finite Element Method (FEM), where Dirichlet and Neumann boundary conditions are weakly enforced. Connections with other standard and mixed FEM approaches are also discussed. The proposed scheme is validated through comparisons with commercial software and simulations using a 2D elasticity model as a demonstrative example.

Citation

• Journal: 2024 IEEE 63rd Conference on Decision and Control (CDC)
• Year: 2024
• Volume:
• Issue:
• Pages: 2676–2681
• Publisher: IEEE
• DOI: 10.1109/cdc56724.2024.10886295

BibTeX

@inproceedings{Ponce_2024,
  title={{Structure-preserving discretization of multidimensional linear port-Hamiltonian systems using FEM approaches}},
  DOI={10.1109/cdc56724.2024.10886295},
  booktitle={{2024 IEEE 63rd Conference on Decision and Control (CDC)}},
  publisher={IEEE},
  author={Ponce, Cristobal and Wu, Yongxin and Gorrec, Yann Le and Ramirez, Hector},
  year={2024},
  pages={2676--2681}
}

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