Sliding mode on tangential sets of Filippov systems
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Acceso en línea: | |
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| _version_ | 1866913475991699456 |
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| author | Carvalho, Tiago Novaes, Douglas D. Tonon, Durval J. |
| author_facet | Carvalho, Tiago Novaes, Douglas D. Tonon, Durval J. |
| contents | We consider piecewise smooth vector fields $Z=(Z_+, Z_-)$ defined in $\mathbb{R}^n$ where both vector fields are tangent to the switching manifold $Σ$ along a submanifold $M\subset Σ$. We shall see that, under suitable assumptions, Filippov convention gives rise to a unique sliding mode on $M$, governed by what we call the {\it tangential sliding vector field}. Here, we will provide the necessary and sufficient conditions for characterizing such a vector field. Additionally, we prove that the tangential sliding vector field is conjugated to the reduced dynamics of a singular perturbation problem arising from the Sotomayor-Teixeira regularization of $Z$ around $M$. Finally, we analyze several examples where tangential sliding vector fields can be observed, including a model for intermittent treatment of HIV. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_12377 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Sliding mode on tangential sets of Filippov systems Carvalho, Tiago Novaes, Douglas D. Tonon, Durval J. Dynamical Systems 34A36, 34A60, 34E15 We consider piecewise smooth vector fields $Z=(Z_+, Z_-)$ defined in $\mathbb{R}^n$ where both vector fields are tangent to the switching manifold $Σ$ along a submanifold $M\subset Σ$. We shall see that, under suitable assumptions, Filippov convention gives rise to a unique sliding mode on $M$, governed by what we call the {\it tangential sliding vector field}. Here, we will provide the necessary and sufficient conditions for characterizing such a vector field. Additionally, we prove that the tangential sliding vector field is conjugated to the reduced dynamics of a singular perturbation problem arising from the Sotomayor-Teixeira regularization of $Z$ around $M$. Finally, we analyze several examples where tangential sliding vector fields can be observed, including a model for intermittent treatment of HIV. |
| title | Sliding mode on tangential sets of Filippov systems |
| topic | Dynamical Systems 34A36, 34A60, 34E15 |
| url | https://arxiv.org/abs/2111.12377 |