Geometric Data-Driven Dimensionality Reduction in MPC with Guarantees
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916212331511808 |
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| author | Schurig, Roland Himmel, Andreas Findeisen, Rolf |
| author_facet | Schurig, Roland Himmel, Andreas Findeisen, Rolf |
| contents | We address the challenge of dimension reduction in the discrete-time optimal control problem which is solved repeatedly online within the framework of model predictive control. Our study demonstrates that a reduced-order approach, aimed at identifying a suboptimal solution within a low-dimensional subspace, retains the stability and recursive feasibility characteristics of the original problem. We present a necessary and sufficient condition for ensuring initial feasibility, which is seamlessly integrated into the subspace design process. Additionally, we employ techniques from optimization on Riemannian manifolds to develop a subspace that efficiently represents a collection of pre-specified high-dimensional data points, all while adhering to the initial admissibility constraint. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02734 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Geometric Data-Driven Dimensionality Reduction in MPC with Guarantees Schurig, Roland Himmel, Andreas Findeisen, Rolf Systems and Control Optimization and Control We address the challenge of dimension reduction in the discrete-time optimal control problem which is solved repeatedly online within the framework of model predictive control. Our study demonstrates that a reduced-order approach, aimed at identifying a suboptimal solution within a low-dimensional subspace, retains the stability and recursive feasibility characteristics of the original problem. We present a necessary and sufficient condition for ensuring initial feasibility, which is seamlessly integrated into the subspace design process. Additionally, we employ techniques from optimization on Riemannian manifolds to develop a subspace that efficiently represents a collection of pre-specified high-dimensional data points, all while adhering to the initial admissibility constraint. |
| title | Geometric Data-Driven Dimensionality Reduction in MPC with Guarantees |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2312.02734 |