Reference Tracking and Observer Design for Space Fractional Partial Differential Equation Modeling Gas Pressures in Fractured Media

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2 Scopus citations

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 stability 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 achieve this, the backstepping approach is adapted to the space FPDEs. The key challenge in this adaptation is the nonapplicability 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.
Original languageEnglish (US)
Pages (from-to)1613-1641
Number of pages29
JournalSIAM Journal on Control and Optimization
Volume60
Issue number3
DOIs
StatePublished - Jun 1 2022

Bibliographical note

KAUST Repository Item: Exported on 2022-06-06

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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