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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.01087 |
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| _version_ | 1866929629427662848 |
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| author | Gernandt, Hannes Schaller, Manuel |
| author_facet | Gernandt, Hannes Schaller, Manuel |
| contents | In this note, we consider port-Hamiltonian structures in numerical optimal control of ordinary differential equations. By introducing a novel class of nonlinear monotone port-Hamiltonian (pH) systems, we show that the primal-dual gradient method may be viewed as an infinite-dimensional nonlinear pH system. The monotonicity and the particular block structure arising in the optimality system is used to prove exponential stability of the dynamics towards its equilibrium, which is a critical point of the first-order optimality conditions. Leveraging the port-based modeling, we propose an optimization-based controller in a suboptimal receding horizon control fashion. To this end, the primal-dual gradient based optimizer-dynamics is coupled to a pH plant dynamics in a power-preserving manner. We show that the resulting model is again monotone pH system and prove that the closed-loop exhibits local exponential convergence towards the equilibrium. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01087 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Port-Hamiltonian structures in infinite-dimensional optimal control: Primal-Dual gradient method and control-by-interconnection Gernandt, Hannes Schaller, Manuel Optimization and Control In this note, we consider port-Hamiltonian structures in numerical optimal control of ordinary differential equations. By introducing a novel class of nonlinear monotone port-Hamiltonian (pH) systems, we show that the primal-dual gradient method may be viewed as an infinite-dimensional nonlinear pH system. The monotonicity and the particular block structure arising in the optimality system is used to prove exponential stability of the dynamics towards its equilibrium, which is a critical point of the first-order optimality conditions. Leveraging the port-based modeling, we propose an optimization-based controller in a suboptimal receding horizon control fashion. To this end, the primal-dual gradient based optimizer-dynamics is coupled to a pH plant dynamics in a power-preserving manner. We show that the resulting model is again monotone pH system and prove that the closed-loop exhibits local exponential convergence towards the equilibrium. |
| title | Port-Hamiltonian structures in infinite-dimensional optimal control: Primal-Dual gradient method and control-by-interconnection |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2406.01087 |