Passivity-based boundary control for stochastic delay reaction–diffusion systems

Abstract

This paper considers the passivity-based boundary control for stochastic delay reaction–diffusion systems (SDRDSs) with boundary input–output. Delay-dependent sufficient conditions are obtained in the sense of expectation for SDRDSs by the use of Lyapunov functional method, for the input strict passivity and the output strict passivity, respectively. Then delay-dependent sufficient conditions are presented to ensure the uncertainty SDRDSs to achieve the robust passivity. Moreover, by utilising the techniques of Green formula and Poincare's inequality, the difficulty is handled caused by the boundary input and boundary controller. Besides, the troubles brought by the existence of the stochastic term and uncertain parameters are resolved by stochastic inequality techniques. Finally, numerical simulations are provided to show the validity of our theoretical results.

Keywords:

• Passivity
• robust passivity
• boundary control
• boundary input–output
• stochastic reaction–diffusion systems

Data availability statement

The data that support the findings of this study are available from the corresponding author: Kai-Ning Wu, upon reasonable request.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by Natural Science Foundations of Shandong Province under Grant ZR2021MF007.

Notes on contributors

Wei-Jie Zhou

Wei-Jie Zhou received the B.S. degree from the Liaocheng Univercity and the M.S. degree from the Harbin Institute of Technology at Weihai, China, in 2019 and 2021 respectively, all in mathematics. She is currently pursuing the Ph.D. degree in mathematics from the Harbin Institute of Technology, Harbin, China. Her research interests include sliding mode control and partial differential systems.

Min Long

Min Long received the B.S. degree in statistics from China University of Mining and Technology, Xuzhou, China, in 2021. She is currently pursuing the M.S. degree in mathematics from the Harbin Institute of Technology at Weihai, China. Her research interests include boundary control and one-dimensional stochastic partial differential systems.

Xiao-Zhen Liu

Xiao-Zhen Liu received the B.S., M.S. degrees from the Harbin Institute of Technology at Weihai, China, and the Ph. D. degrees from the Harbin Institute of Technology, Harbin, Helongjiang, China, in 2015, 2017 and 2022 respectively, all in mathematics. She is currently with School of Mathematics and Statistics, Shandong University, Weihai, as a research assistant. Her research interests include stochastic control and partial differential systems.

Kai-Ning Wu

Kai-Ning Wu received the B.S., M.S., and Ph. D. degrees from the Harbin Institute of Technology, Harbin, Helongjiang, China, in 2003, 2005 and 2009 respectively, all in mathematics. He is currently with the Department of Mathematics, Harbin Institute of Technology at Weihai, China, as an associate professor. His research interests include robust control, stochastic control and delay differential systems.