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- W4287144471 abstract "Constructing differentiation algorithms with a fixed-time convergence and a predefined Upper Bound on their Settling Time (textit{UBST}), i.e., predefined-time differentiators, is attracting attention for solving estimation and control problems under time constraints. However, existing methods are limited to signals having an $n$-th Lipschitz derivative. Here, we introduce a general methodology to design $n$-th order predefined-time differentiators for a broader class of signals: for signals, whose $(n+1)$-th derivative is bounded by a function with bounded logarithmic derivative, i.e., whose $(n+1)$-th derivative grows at most exponentially. Our approach is based on a class of time-varying gains known as Time-Base Generators (textit{TBG}). The only assumption to construct the differentiator is that the class of signals to be differentiated $n$-times have a $(n+1)$-th derivative bounded by a known function with a known bound for its $(n+1)$-th logarithmic derivative. We show how our methodology achieves an textit{UBST} equal to the predefined time, better transient responses with smaller error peaks than autonomous predefined-time differentiators, and a textit{TBG} gain that is bounded at the settling time instant." @default.
- W4287144471 created "2022-07-25" @default.
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- W4287144471 date "2021-06-01" @default.
- W4287144471 modified "2023-09-29" @default.
- W4287144471 title "An arbitrary-order predefined-time exact differentiator for signals with exponential growth bound" @default.
- W4287144471 doi "https://doi.org/10.48550/arxiv.2106.00822" @default.
- W4287144471 hasPublicationYear "2021" @default.
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