Observer Design for Semilinear Time Fractional Diffusion Systems with Spatially Varying Parameters

6 Pages Posted: 9 Nov 2018

See all articles by Fudong Ge

Fudong Ge

China University of Geosciences

Yang Quan Chen

University of California, Merced

Date Written: July 1, 2018

Abstract

This paper describes how to design observers for the semilinear time fractional diffusion systems with spatially varying parameters. The motivation is that the availability of full-state measurements in some practical cases may be impossible for direct measurement due to the difficulties in measuring. For this, an integral transformation is first proposed to equivalently convert the considered systems into a simpler form with Robin boundary conditions. Besides, we build an extended Luenbergertype observer that uses measurements of the inputs and the outputs of system under consideration to determine its state. MittagLeffler stabilization problem of the corresponding semilinear observer error dynamic systems is then explored via backstepping technique. A numerical illustration is finally included.

Keywords: Semilinear Time Fractional Diffusion Systems; Observer Design Problems; Mittag-Leffler Stability; Backstepping

Suggested Citation

Ge, Fudong and Chen, Yang Quan, Observer Design for Semilinear Time Fractional Diffusion Systems with Spatially Varying Parameters (July 1, 2018). Proceedings of International Conference on Fractional Differentiation and its Applications (ICFDA) 2018. Available at SSRN: https://ssrn.com/abstract=3281639 or http://dx.doi.org/10.2139/ssrn.3281639

Fudong Ge (Contact Author)

China University of Geosciences ( email )

Wuhan, China
Wuhan, Hubei
China

Yang Quan Chen

University of California, Merced ( email )

P.O. Box 2039
Merced, CA 95344
United States

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