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dc.contributor.authorGhaffour, Lilia
dc.contributor.authorLaleg-Kirati, Taous-Meriem
dc.date.accessioned2021-07-12T06:25:53Z
dc.date.available2021-07-12T06:25:53Z
dc.date.issued2021-07-05
dc.identifier.urihttp://hdl.handle.net/10754/670127
dc.description.abstractThis 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.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2107.02042.pdf
dc.rightsArchived with thanks to arXiv
dc.subjectReference Tracking
dc.subjectObserver Design
dc.subjectFractional systems
dc.subjectWell-posedness
dc.subjectUniqueness
dc.titleReference Tracking AND Observer Design for Space-Fractional Partial Differential Equation Modeling Gas Pressures in Fractured Media
dc.typePreprint
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputational Bioscience Research Center (CBRC)
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
dc.contributor.departmentElectrical and Computer Engineering Program
dc.contributor.departmentEstimation, Modeling and ANalysis Group
dc.eprint.versionPre-print
dc.contributor.institutionNational Institute for Research in Digital Science and Technology (INRIA), France .
dc.identifier.arxivid2107.02042
kaust.personGhaffour, Lilia
kaust.personLaleg-Kirati, Taous-Meriem
refterms.dateFOA2021-07-12T06:28:26Z


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