A Simulation Preorder for Koopman-like Lifted Control Systems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929368926781440 |
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| author | Aspeel, Antoine Ozay, Necmiye |
| author_facet | Aspeel, Antoine Ozay, Necmiye |
| contents | This paper introduces a simulation preorder among lifted systems, a generalization of finite-dimensional Koopman approximations (also known as approximate immersions) to systems with inputs. It is proved that this simulation relation implies the containment of both the open- and closed-loop behaviors. Optimization-based sufficient conditions are derived to verify the simulation relation in two special cases: i) a nonlinear (unlifted) system and an affine lifted system and, ii) two affine lifted systems. Numerical examples demonstrate the approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14909 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Simulation Preorder for Koopman-like Lifted Control Systems Aspeel, Antoine Ozay, Necmiye Systems and Control Optimization and Control This paper introduces a simulation preorder among lifted systems, a generalization of finite-dimensional Koopman approximations (also known as approximate immersions) to systems with inputs. It is proved that this simulation relation implies the containment of both the open- and closed-loop behaviors. Optimization-based sufficient conditions are derived to verify the simulation relation in two special cases: i) a nonlinear (unlifted) system and an affine lifted system and, ii) two affine lifted systems. Numerical examples demonstrate the approach. |
| title | A Simulation Preorder for Koopman-like Lifted Control Systems |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2401.14909 |