5 research outputs found
Reference Tracking AND Observer Design for Space-Fractional Partial Differential Equation Modeling Gas Pressures in Fractured Media
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 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.Comment: 37 pages, 9 figure
Non-asymptotic state estimation of linear reaction diffusion equation using modulating functions
In this paper, we propose a non-asymptotic state estimation method for the linear reaction diffusion equation with general boundary conditions. The method is based on the modulating function approach utilizing a modulation functional in time and space. This results in a signal model control problem for a system of auxiliary PDEs in order to determine the modulation kernels. First, the algorithm is mathematically derived and then numerical simulations are presented for illustrating the good performance of the proposed approach and demonstrating the efficient implementation scheme