Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/39324
Title: | Regional gradient observability for fractional differential equations with Caputo time-fractional derivatives |
Author: | Zguaid, Khalid El Alaoui, Fatima-Zahrae Torres, Delfim F. M. |
Keywords: | Distributed parameter systems Control theory Fractional calculus Regional analysis Gradient observability Gradient strategic sensors |
Issue Date: | 2023 |
Publisher: | Springer |
Abstract: | We investigate the regional gradient observability of fractional sub-diffusion equations involving the Caputo derivative. The problem consists of describing a method to find and recover the initial gradient vector in the desired region, which is contained in the spatial domain. After giving necessary notions and definitions, we prove some useful characterizations for exact and approximate regional gradient observability. An example of a fractional system that is not (globally) gradient observable but it is regionally gradient observable is given, showing the importance of regional analysis. Our characterization of the notion of regional gradient observability is given for two types of strategic sensors. The recovery of the initial gradient is carried out using an expansion of the Hilbert uniqueness method. Two illustrative examples are given to show the application of the developed approach. The numerical simulations confirm that the proposed algorithm is effective in terms of the reconstruction error. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/39324 |
DOI: | 10.1007/s40435-022-01106-0 |
ISSN: | 2195-268X |
Appears in Collections: | CIDMA - Artigos DMat - Artigos SCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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[524]Zguaid_El-Alaoui_Torres-IJDY.pdf | 601.08 kB | Adobe PDF | View/Open |
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