Neumann boundary geometric control of a fractional diffusion process Online publication date: Thu, 06-Aug-2020
by Ahmed Maidi; Jean-Pierre Corriou
International Journal of Modelling, Identification and Control (IJMIC), Vol. 34, No. 1, 2020
Abstract: In this paper, a boundary controller is developed for the fractional diffusion equation in the framework of geometric control. The case of Neumann actuation with a spatial weighted average output is addressed. This non-collocated configuration is characterised by an infinite characteristic index. To overcome this difficulty, the notion of the extended operator is exploited to derive an equivalent distributed control problem. The equivalent model, obtained by the Laplace transform in space domain, is used both for controller design and stability analysis of the resulting closed-loop. Thus, based on the notion of the characteristic index, a state feedback control that enforces an output tracking is designed. Then, the exponential stability of the closed-loop is demonstrated based on the semigroup theory. The effectiveness of the developed controller is shown, through numerical simulation, in the case of a heated aluminium rod that exhibits an anomalous diffusion phenomenon.
Online publication date: Thu, 06-Aug-2020
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Modelling, Identification and Control (IJMIC):
Login with your Inderscience username and password:
Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.
If you still need assistance, please email email@example.com