Paper Info
Title
Feedback stabilization of a 1D linear reaction-diffusion equation with delay boundary control
Abstract
The goal of this paper is to design a stabilizing feedback boundary control for a reaction–diffusion partial differential equation (PDE), where the boundary control is subject to a constant delay while the equation may be unstable without any control. For this system, which is equivalent to a parabolic equation coupled with a transport equation, a prediction-based control is explicitly computed by splitting the infinite-dimensional system into two parts: a finite-dimensional unstable part and a stable infinite-dimensional part. A finite-dimensional delayed controller is computed for the unstable part, and it is shown that this controller stabilizes the whole PDE. The proof is based on an explicit expression of the classical Artstein transformation combined with an adequately designed Lyapunov function. A numerical simulation illustrates the constructive feedback design method.
Year
DOI
Venue
2019
10.1109/tac.2018.2849560
IEEE Transactions on Automatic Control
Keywords
DocType
Volume
Delays,Control systems,Mathematical model,Feedback control,Design methodology,Partial differential equations,Lyapunov methods
Journal
64
Issue
ISSN
Citations 
4
0018-9286
6
PageRank 
References 
Authors
0.46
7
2
Name
Order
Citations
PageRank
Christophe Prieur11037129.96
Emmanuel Trélat218324.42