dc.contributor.author Ghaffour, Lilia dc.contributor.author Laleg-Kirati, Taous-Meriem dc.date.accessioned 2021-07-12T06:25:53Z dc.date.available 2021-07-12T06:25:53Z dc.date.issued 2021-07-05 dc.identifier.uri http://hdl.handle.net/10754/670127 dc.description.abstract This paper considers a class of space fractional partial differential equations (FPDEs) that describe gas pressures in fractured media. First, the well-posedness, uniqueness, and the stability in $L_(\infty{R})$of the considered FPDEs are investigated. Then, the reference tracking problem is studied to track the pressure gradient at a downstream location of a channel. This requires manipulation of gas pressure at the downstream location and the use of pressure measurements at an upstream location. To achiever this, the backstepping approach is adapted to the space FPDEs. The key challenge in this adaptation is the non-applicability of the Lyapunov theory which is typically used to prove the stability of the target system as, the obtained target system is fractional in space. In addition, a backstepping adaptive observer is designed to jointly estimate both the system's state and the disturbance. The stability of the closed loop (reference tracking controller/observer) is also investigated. Finally, numerical simulations are given to evaluate the efficiency of the proposed method. dc.publisher arXiv dc.relation.url https://arxiv.org/pdf/2107.02042.pdf dc.rights Archived with thanks to arXiv dc.subject Reference Tracking dc.subject Observer Design dc.subject Fractional systems dc.subject Well-posedness dc.subject Uniqueness dc.title Reference Tracking AND Observer Design for Space-Fractional Partial Differential Equation Modeling Gas Pressures in Fractured Media dc.type Preprint dc.contributor.department Applied Mathematics and Computational Science Program dc.contributor.department Computational Bioscience Research Center (CBRC) dc.contributor.department Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division dc.contributor.department Electrical and Computer Engineering Program dc.contributor.department Estimation, Modeling and ANalysis Group dc.eprint.version Pre-print dc.contributor.institution National Institute for Research in Digital Science and Technology (INRIA), France . dc.identifier.arxivid 2107.02042 kaust.person Ghaffour, Lilia kaust.person Laleg-Kirati, Taous-Meriem refterms.dateFOA 2021-07-12T06:28:26Z
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