Observer-based output feedback control design for a coupled system of fractional ordinary and reaction–diffusion equations. (16th March 2020)

• Record Type: Journal Article
• Authors: Amiri, Shadi; Keyanpour, Mohammad; Asaraii, Asadollah
• Is Part Of: IMA journal of mathematical control and information. Volume 38:Number 1(2021)
• Page Start: 90
• Page End: 124
• Publication Date: 2020-03-16
• Subjects: observer design -- output feedback control design -- cascaded fractional-order systems -- backstepping; Control theory -- Periodicals; 629.831205
• DOI: 10.1093/imamci/dnaa002
• Languages: English
• ISSNs: 0265-0754

Abstract

Abstract: In this paper, we investigate the stabilization problem of a cascade of a fractional ordinary differential equation (FODE) and a fractional reaction–diffusion (FRD) equation where the interconnections are of Neumann type. We exploit the partial differential equation backstepping method for designing a controller, which guarantees the Mittag–Leffler stability of the FODE-FRD cascade. Moreover, we propose an observer that is Mittag–Leffler convergent. Also, we propose an output feedback boundary controller, and we prove that the closed-loop FODE-FRD system is Mittag–Leffler stable in the sense of the corresponding norm. Finally, numerical simulations are presented to verify the results.