A Mixed-FEM approximation with uniform conservation of the exponential stability for a class of anisotropic port-Hamiltonian system and its application to LQ control
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909545870131200 |
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| author | Mora, Luis A. Morris, Kirsten |
| author_facet | Mora, Luis A. Morris, Kirsten |
| contents | In this manuscript, we present a mixed finite element discretization for a class of boundary-damped anisotropic port-Hamiltonian systems. Using a multiplier method, we demonstrate that the resulting approximation model uniformly preserves the exponential stability of the uncontrolled system, establishing a lower bound for the exponential decay rate that is independent of the mesh size. This property is illustrated through the spatial discretization of a piezoelectric beam. Furthermore, we show how the uniform preservation of exponential stability by the proposed model aids in the convergence of controllers derived from an infinite-time linear quadratic control design, in comparison to models obtained from the standard finite-element method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_16388 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Mixed-FEM approximation with uniform conservation of the exponential stability for a class of anisotropic port-Hamiltonian system and its application to LQ control Mora, Luis A. Morris, Kirsten Numerical Analysis Analysis of PDEs Dynamical Systems Optimization and Control In this manuscript, we present a mixed finite element discretization for a class of boundary-damped anisotropic port-Hamiltonian systems. Using a multiplier method, we demonstrate that the resulting approximation model uniformly preserves the exponential stability of the uncontrolled system, establishing a lower bound for the exponential decay rate that is independent of the mesh size. This property is illustrated through the spatial discretization of a piezoelectric beam. Furthermore, we show how the uniform preservation of exponential stability by the proposed model aids in the convergence of controllers derived from an infinite-time linear quadratic control design, in comparison to models obtained from the standard finite-element method. |
| title | A Mixed-FEM approximation with uniform conservation of the exponential stability for a class of anisotropic port-Hamiltonian system and its application to LQ control |
| topic | Numerical Analysis Analysis of PDEs Dynamical Systems Optimization and Control |
| url | https://arxiv.org/abs/2503.16388 |