On Structural Non-commutativity in Affine Feedback of SISO Nonlinear Systems
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911814317506560 |
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| author | S., Venkatesh G. |
| author_facet | S., Venkatesh G. |
| contents | The affine feedback connection of SISO nonlinear systems modeled by Chen--Fliess series is shown to be a group action on the plant which is isomorphic to the semi-direct product of shuffle and additive group of non-commutative formal power series. The additive and multiplicative feedback loops in an affine feedback connection are thus proven to be structurally non-commutative. A flip in the order of these loops results in a net additive feedback loop. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17730 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Structural Non-commutativity in Affine Feedback of SISO Nonlinear Systems S., Venkatesh G. Optimization and Control Systems and Control The affine feedback connection of SISO nonlinear systems modeled by Chen--Fliess series is shown to be a group action on the plant which is isomorphic to the semi-direct product of shuffle and additive group of non-commutative formal power series. The additive and multiplicative feedback loops in an affine feedback connection are thus proven to be structurally non-commutative. A flip in the order of these loops results in a net additive feedback loop. |
| title | On Structural Non-commutativity in Affine Feedback of SISO Nonlinear Systems |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2403.17730 |