Designing predefined-time differentiators with bounded time-varying gains
| Autor: | Aldana-López, Rodrigo, Seeber, Richard, Gómez-Gutiérrez, David, Angulo, Marco Tulio, Defoort, Michael |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | International Journal of Robust and Nonlinear Control, 2022 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1002/rnc.6315 |
| Popis: | There is an increasing interest in designing differentiators, which converge exactly before a prespecified time regardless of the initial conditions, i.e., which are fixed-time convergent with a predefined Upper Bound of their Settling Time (UBST), due to their ability to solve estimation and control problems with time constraints. However, for the class of signals with a known bound of their $(n+1)$-th time derivative, the existing design methodologies yield a very conservative UBST, or result in gains that tend to infinity at the convergence time. Here, we introduce a new methodology based on time-varying gains to design arbitrary-order exact differentiators with a predefined UBST. This UBST is a priori set as one parameter of the algorithm. Our approach guarantees that the UBST can be set arbitrarily tight, and we also provide sufficient conditions to obtain exact convergence while maintaining bounded time-varying gains. Additionally, we provide necessary and sufficient conditions such that our approach yields error dynamics with a uniformly Lyapunov stable equilibrium. Our results show how time-varying gains offer a general and flexible methodology to design algorithms with a predefined UBST. Comment: This is the preprint version of the accepted manuscript with DOI: 10.1002/rnc.6315. Please cite the publisher's version. For the publisher's version and full citation details, see: https://doi.org/10.1002/rnc.6315. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions |
| Databáze: | arXiv |
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