Controllability of periodic linear systems, the Poincare sphere, and quasi-affine systems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866908492359532544 |
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| author | Colonius, Fritz Santana, Alexandre Setti, Juliana |
| author_facet | Colonius, Fritz Santana, Alexandre Setti, Juliana |
| contents | For periodic linear control systems with bounded control range, an autonomized system is introduced by adding the phase to the state of the system. Here a unique control set (i.e., a maximal set of approximate controllability) with nonvoid interior exists. It is determined by the spectral subspaces of the homogeneous part which is a periodic linear differential equation. Using the Poincaré sphere one obtains a compactification of the state space allowing us to describe the behavior near infinity of the original control system. Furthermore, an application to quasi-affine systems yields a unique control set with nonvoid interior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_05308 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Controllability of periodic linear systems, the Poincare sphere, and quasi-affine systems Colonius, Fritz Santana, Alexandre Setti, Juliana Optimization and Control 93B05, 34H05 For periodic linear control systems with bounded control range, an autonomized system is introduced by adding the phase to the state of the system. Here a unique control set (i.e., a maximal set of approximate controllability) with nonvoid interior exists. It is determined by the spectral subspaces of the homogeneous part which is a periodic linear differential equation. Using the Poincaré sphere one obtains a compactification of the state space allowing us to describe the behavior near infinity of the original control system. Furthermore, an application to quasi-affine systems yields a unique control set with nonvoid interior. |
| title | Controllability of periodic linear systems, the Poincare sphere, and quasi-affine systems |
| topic | Optimization and Control 93B05, 34H05 |
| url | https://arxiv.org/abs/2212.05308 |