On driftless systems with m controls and 2m or 2m - 1 states that are flat by pure prolongation
It is widely recognized that no tractable necessary and sufficient conditions exist for determining whether a system is, in general, differentially flat. However, specific cases do provide such conditions. For instance, driftless systems with two inputs have known necessary and sufficient conditions...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/455216 |
| Acceso en línea: | https://hdl.handle.net/2117/455216 https://dx.doi.org/10.1142/S297245892540012X |
| Access Level: | acceso abierto |
| Palabra clave: | System theory Nonlinear control systems differential geometric control Lie bracket driftless system differential flatness pure prolongation Sistemes de control Classificació AMS::93 Systems Theory Control::93C Control systems, guided systems Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa |
| Sumario: | It is widely recognized that no tractable necessary and sufficient conditions exist for determining whether a system is, in general, differentially flat. However, specific cases do provide such conditions. For instance, driftless systems with two inputs have known necessary and sufficient conditions. For driftless systems with three or more inputs, the available conditions are only sufficient. This paper presents new findings on determining whether a system with [Formula: see text] inputs and [Formula: see text] or [Formula: see text] states is flat by pure prolongation, a specific subclass of differential flatness. While this condition is more restrictive than general differential flatness, the algorithm for computing flat outputs remains remarkably simple, and the verification requirements are relatively lenient. Moreover, the conditions proposed in this work broaden the class of systems recognized as differentially flat, as our sufficient condition differs from existing criteria. |
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