Geometric control and disturbance decoupling for fractional systems
We develop a geometric approach for fractional linear time-invariant systems with Caputo-type derivatives. In particular, we generalize the fundamental notions of invariance and controlled invariance to the fractional setting. We then exploit this new geometric framework to address the disturbance d...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Language: | English |
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SIAM PUBLICATIONS
2020
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/89487 |
| _version_ | 1848765230553759744 |
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| author | Padula, Fabrizio Ntogramatzidis, Lorenzo Schmid, R. Loxton, Ryan |
| author_facet | Padula, Fabrizio Ntogramatzidis, Lorenzo Schmid, R. Loxton, Ryan |
| author_sort | Padula, Fabrizio |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We develop a geometric approach for fractional linear time-invariant systems with Caputo-type derivatives. In particular, we generalize the fundamental notions of invariance and controlled invariance to the fractional setting. We then exploit this new geometric framework to address the disturbance decoupling problem via static pseudostate feedback, with and without stability. Our main contribution is a set of necessary and sufficient conditions for the disturbance decoupling problem that are related to the input-output properties of the closed-loop system, and hence they are applicable not just to Caputo-type derivatives but, more broadly, to any type of fractional system. These results show that, while the conditions for guaranteeing the existence of a decoupling pseudostate feedback remain essentially unchanged, the underlying theoretical framework is substantially different, because the fractional derivative is a nonlocal operator and this property plays a major role in the characterization of the evolution of the pseudostate trajectory. In particular, we show that, unlike the integer case, the infinite-dimensional nature of fractional systems means that feedback control is insufficient to maintain the pseudostate trajectory on a controlled invariant subspace, unless the entire past history of the pseudostate has evolved on that subspace. However, feedforward control can achieve this task under certain necessary and sufficient geometric conditions. |
| first_indexed | 2025-11-14T11:31:57Z |
| format | Journal Article |
| id | curtin-20.500.11937-89487 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:31:57Z |
| publishDate | 2020 |
| publisher | SIAM PUBLICATIONS |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-894872023-06-13T05:54:10Z Geometric control and disturbance decoupling for fractional systems Padula, Fabrizio Ntogramatzidis, Lorenzo Schmid, R. Loxton, Ryan Science & Technology Technology Physical Sciences Automation & Control Systems Mathematics, Applied Mathematics controlled invariance disturbance decoupling fractional systems CONTROLLABILITY OBSERVABILITY ASSIGNMENT TRANSIENTS We develop a geometric approach for fractional linear time-invariant systems with Caputo-type derivatives. In particular, we generalize the fundamental notions of invariance and controlled invariance to the fractional setting. We then exploit this new geometric framework to address the disturbance decoupling problem via static pseudostate feedback, with and without stability. Our main contribution is a set of necessary and sufficient conditions for the disturbance decoupling problem that are related to the input-output properties of the closed-loop system, and hence they are applicable not just to Caputo-type derivatives but, more broadly, to any type of fractional system. These results show that, while the conditions for guaranteeing the existence of a decoupling pseudostate feedback remain essentially unchanged, the underlying theoretical framework is substantially different, because the fractional derivative is a nonlocal operator and this property plays a major role in the characterization of the evolution of the pseudostate trajectory. In particular, we show that, unlike the integer case, the infinite-dimensional nature of fractional systems means that feedback control is insufficient to maintain the pseudostate trajectory on a controlled invariant subspace, unless the entire past history of the pseudostate has evolved on that subspace. However, feedforward control can achieve this task under certain necessary and sufficient geometric conditions. 2020 Journal Article http://hdl.handle.net/20.500.11937/89487 10.1137/19M1261493 English SIAM PUBLICATIONS fulltext |
| spellingShingle | Science & Technology Technology Physical Sciences Automation & Control Systems Mathematics, Applied Mathematics controlled invariance disturbance decoupling fractional systems CONTROLLABILITY OBSERVABILITY ASSIGNMENT TRANSIENTS Padula, Fabrizio Ntogramatzidis, Lorenzo Schmid, R. Loxton, Ryan Geometric control and disturbance decoupling for fractional systems |
| title | Geometric control and disturbance decoupling for fractional systems |
| title_full | Geometric control and disturbance decoupling for fractional systems |
| title_fullStr | Geometric control and disturbance decoupling for fractional systems |
| title_full_unstemmed | Geometric control and disturbance decoupling for fractional systems |
| title_short | Geometric control and disturbance decoupling for fractional systems |
| title_sort | geometric control and disturbance decoupling for fractional systems |
| topic | Science & Technology Technology Physical Sciences Automation & Control Systems Mathematics, Applied Mathematics controlled invariance disturbance decoupling fractional systems CONTROLLABILITY OBSERVABILITY ASSIGNMENT TRANSIENTS |
| url | http://hdl.handle.net/20.500.11937/89487 |