Finite-time synchronization of delayed semi-Markov reaction-diffusion systems: An asynchronous boundary control scheme

Angang Wei; Zhongyuan Yao; Yu Zhang; Kaiming Wang

doi:10.1016/j.isatra.2024.03.030

Finite-time synchronization of delayed semi-Markov reaction-diffusion systems: An asynchronous boundary control scheme

ISA Trans. 2024 Mar 27:S0019-0578(24)00138-1. doi: 10.1016/j.isatra.2024.03.030. Online ahead of print.

Authors

Angang Wei¹, Zhongyuan Yao², Yu Zhang³, Kaiming Wang⁴

Affiliations

¹ China Huaneng Group Clean Energy Technology Research Institute Co., Ltd., China; Department of Mechanical Engineering, Tsinghua University, Beijing 102209, China. Electronic address: waa16@tsinghua.org.cn.
² Jiangsu Clean Energy Branch of Huaneng International Power Co., Ltd., Nanjing 210005, China. Electronic address: yzyhuangneng@126.com.
³ Jiangsu Clean Energy Branch of Huaneng International Power Co., Ltd., Nanjing 210005, China. Electronic address: weidexiaomi@163.com.
⁴ Hunan Provincial Key Laboratory of Intelligent Manufacturing Technology for High-performance Mechanical Equipment, Changsha University of Science and Technology, Changsha 410114, China; Key Laboratory of Vibration and Control of Aero-Propulsion System, Ministry of Education, Northeastern University, Shenyang 110819, China. Electronic address: kmwang@csust.edu.cn.

PMID: 38570256
DOI: 10.1016/j.isatra.2024.03.030

Abstract

This paper tries to study the problem of finite-time synchronization for delayed semi-Markov reaction-diffusion systems. Based on the spatial and parametric characteristics of the considered systems, a new asynchronous boundary control scheme is proposed to ensure the finite-time synchronization of the drive and response systems. In the asynchronous boundary control scheme, only an actuator should be placed at the spatial boundary, which is more easier to implement and economical than the other non-boundary control strategies. Besides, the system parameters and controller follow two asynchronous semi-Markov chains for jumping, which is more practical than obeying one semi-Markov chain. Moreover, for the considered systems, we proposes a new lemma of finite-time stability, and by employing the inequality methods and variable substitution, we derive the criterion of finite-time synchronization and a correlative corollary. Finally, a numerical example and an application example on secure communication are carried out to support the developed approach.

Keywords: Asynchronous boundary control; Finite-time synchronization; Reaction–diffusion systems; Secure communication; Semi-Markov switching parameters.