Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 64, Issue 4, Pages 1415-1425Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2018.2849560
Keywords
delay control; Lyapunov function; partial differential equation (PDE); Reaction-diffusion equation
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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.
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