Journal
IET CONTROL THEORY AND APPLICATIONS
Volume 12, Issue 11, Pages 1561-1572Publisher
INST ENGINEERING TECHNOLOGY-IET
DOI: 10.1049/iet-cta.2017.1352
Keywords
stability; reaction-diffusion systems; Lyapunov methods; nonlinear control systems; closed loop systems; feedback; asymptotic stability; control system synthesis; diffusion; observers; partial differential equations; control nonlinearities; fractional reaction diffusion system; observer design; considered FRD system; boundary measurable; actuation; nonconstant diffusivity; output feedback controller; closed-loop FRD systems; boundary feedback controller; observer error system; Mittag-Leffler stable target system; observer gains; output feedback control law; closed-loop system
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Funding
- National Natural Science Foundation of China [61174021, 61473136]
- Fundamental Research Funds for the Central Universities [JUSRP51322B]
- 111 Project [B12018]
- Jiangsu Innovation Program for Graduates [KYLX15_1167, KYLX15_1170]
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This study is concerned with observer design and observer-based output feedback control for a fractional reaction diffusion (FRD) system with a spatially-varying (non-constant) diffusion coefficient by the backstepping method. The considered FRD system is endowed with only boundary measurable and actuation available. The contribution of this study is divided into three parts: first is the backstepping-based observer design for the FRD system with non-constant diffusivity, second is the output feedback controller generated by the integration of a separately backstepping-based feedback controller and the proposed observer to stabilise the FRD system with non-constant diffusivity, and the last is the Mittag-Leffler stability analysis of the observer error and the closed-loop FRD systems. Specifically, anti-collocated location of actuator and sensor is considered in the stabilisation problem of this system with Robin boundary condition at . By designing an invertible coordinate transformation to convert the observer error system into a Mittag-Leffler stable target system, the observer gains are obtained. They are used to design the output feedback control law for stabilising the closed-loop system. Finally, a numerical example is shown to validate the effectiveness of the authors' proposed method.
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