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Regional boundary observability for Riemann–Liouville linear fractional evolution systems

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  • Zguaid, Khalid
  • El Alaoui, Fatima-Zahrae

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.

Suggested Citation

  • Zguaid, Khalid & El Alaoui, Fatima-Zahrae, 2022. "Regional boundary observability for Riemann–Liouville linear fractional evolution systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 272-286.
    • Handle: RePEc:eee:matcom:v:199:y:2022:i:c:p:272-286
    DOI: 10.1016/j.matcom.2022.03.023
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    1. Zguaid, Khalid & El Alaoui, Fatima Zahrae & Boutoulout, Ali, 2021. "Regional observability for linear time fractional systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 77-87.
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