Boundary control for prescribed-time stabilisation of delayed parabolic reaction-diffusion systems
by Qian Ye; Wei Wu
International Journal of Modelling, Identification and Control (IJMIC), Vol. 44, No. 4, 2024

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.

Online publication date: Thu, 13-Jun-2024

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