Regional boundary observability for Riemann–Liouville linear fractional evolution systems

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 r...

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Bibliographic Details
Published in:Mathematics and computers in simulation 2022-09, Vol.199, p.272-286
Main Authors: Zguaid, Khalid, El Alaoui, Fatima-Zahrae
Format: Article
Language:English
Subjects:
Control theory
Fractional calculus
HUM approach
Regional boundary observability
Time-fractional systems
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Summary: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.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2022.03.023