Title: Boundary control for prescribed-time stabilisation of delayed parabolic reaction-diffusion systems

Authors: Qian Ye; Wei Wu

Addresses: College of IoT Technology, Wuxi Institute of Technology, Wuxi 214121, China ' College of IoT Technology, Wuxi Institute of Technology, Wuxi 214121, China

Abstract: This work addresses the boundary control problem for prescribed-time stabilisation of a parabolic reaction-diffusion system (PRDS) with time delay via the backstepping-based approach and Razumikhin method. The invertible Volterra transformation is used to convert the PRDS into a suitable prescribed-time stable PRDS with time-dependent coefficient, which is related to time-dependent kernel function. The obtained kernel partial differential equations are proven to be well-posed using the successive approximation. The boundary controller is designed by solving the kernel equations to guarantee the prescribed-time stabilisation of the delayed PRDS. Finally, two numerical examples are given to testify the feasibility of the proposed methodology.

Keywords: reaction-diffusion system; distributed parameter system; boundary control; time delay; prescribed-time stabilisation; backstepping approach; Razumikhin method.

DOI: 10.1504/IJMIC.2024.139092

International Journal of Modelling, Identification and Control, 2024 Vol.44 No.4, pp.315 - 327

Received: 15 Oct 2022
Accepted: 10 Feb 2023
Published online: 13 Jun 2024 *

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