 Regional boundary observability for Riemann–Liouville linear fractional evolution systemsKhalid Zguaid and Fatima-Zahrae El Alaoui Mathematics and Computers in Simulation (MATCOM), 2022, vol. 199, issue C, 272-286 Abstract: This paper deals with regional boundary observability of linear time-fractional systems with Riemann–Liouville derivative. The main purpose is to reconstruct the initial state of the considered system in a subregion B of the boundary ∂Ω of the evolution domain Ω. For that, we show the link between regional boundary observability on B and regional observability, of the considered system, in a suitable subregion (ω⊂Ω) defined such that B⊂∂ω. This will allow us to firstly recover the initial state in the subregion ω by using an extension of Hilbert Uniqueness Method for fractional systems, after that we take the restriction, on B, of its trace, on ∂ω, in order to obtain the initial state on B. We also propose an algorithm that enables us to recover the initial state in ω and eventually on B, with a satisfying reconstruction error, which is illustrated in two numerical simulations, using a zonal sensor and a pointwise one. Keywords: Regional boundary observability; Time-fractional systems; Fractional calculus; HUM approach; Control theory (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:199:y:2022:i:c:p:272-286 DOI: 10.1016/j.matcom.2022.03.023 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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