A Flat Triangular Structure Based on a Multi-Chained Form
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917079980965888 |
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| author | Hartl, Georg Gstöttner, Conrad Schöberl, Markus |
| author_facet | Hartl, Georg Gstöttner, Conrad Schöberl, Markus |
| contents | Determining whether a nonlinear multi-input system is differentially flat remains challenging. One way to obtain computationally tractable sufficient conditions is to give complete characterizations of flat normal forms. We introduce a structurally flat triangular form for control-affine systems with at least three inputs that is based on a multi-chained form. For two specific instances of this structure, we provide complete geometric characterizations, i.e., necessary and sufficient conditions under which a control-affine system is static-feedback equivalent to the respective triangular form. These characterizations yield sufficient conditions for differential flatness and, in turn, constructive procedures for computing flat outputs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26632 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Flat Triangular Structure Based on a Multi-Chained Form Hartl, Georg Gstöttner, Conrad Schöberl, Markus Dynamical Systems Determining whether a nonlinear multi-input system is differentially flat remains challenging. One way to obtain computationally tractable sufficient conditions is to give complete characterizations of flat normal forms. We introduce a structurally flat triangular form for control-affine systems with at least three inputs that is based on a multi-chained form. For two specific instances of this structure, we provide complete geometric characterizations, i.e., necessary and sufficient conditions under which a control-affine system is static-feedback equivalent to the respective triangular form. These characterizations yield sufficient conditions for differential flatness and, in turn, constructive procedures for computing flat outputs. |
| title | A Flat Triangular Structure Based on a Multi-Chained Form |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2510.26632 |