Controllability to rest of the Gurtin-Pipkin model

Xiuxiang Zhou; Shu Luan

doi:10.3934/mcrf.2021051

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2022, Volume 12, Issue 3: 831-845. Doi: 10.3934/mcrf.2021051

This issue Previous Article Computation of open-loop inputs for uniformly ensemble controllable systems Next Article

Controllability to rest of the Gurtin-Pipkin model

Xiuxiang Zhou^, and
Shu Luan

School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang, 524048, China

^* Corresponding author: Xiuxiang Zhou
^* Corresponding author: Xiuxiang Zhou

Received: March 31, 2021

Revised: July 31, 2021

Early access: October 2021

Published: July 2022

The first author is supported by the National Natural Science Foundation of China under grants 11926331, 11926337 and 11601213, and by the Foundation for Talents of Lingnan Normal University under grant ZL1612. The second author is supported by the Natural Science Foundation of Guangdong Province under grant 2018A0303070012

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Abstract

This paper is devoted to analyzing the controllability to rest of the Gurtin-Pipkin model, which is a class of differential equations with memory terms. The goal is not only to derive the state to vanish at some time but also to require the memory term to vanish at the same time, ensuring that the controlled system is controllable to rest. In order to get rid of the influence of memory, the controllability result is obtained by means of the Fourier type approach and the moment theory.

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Mathematics Subject Classification: Primary: 93B05; Secondary: 45K05.

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References

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