Synchronization of stochastic reaction–diffusion systems via boundary control

Kai Ning Wu; Jian Wang; Cheng Chew Lim

doi:10.1007/s11071-018-4455-z

Synchronization of stochastic reaction–diffusion systems via boundary control

Kai Ning Wu^*
, Jian Wang
, Cheng Chew Lim

^*Corresponding author for this work

Harbin Institute of Technology Weihai
Adelaide University

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

This paper studies the problem of mean square asymptotical synchronization and H_∞ synchronization for coupled stochastic reaction–diffusion systems (SRDSs) via boundary control. Based on the deduced synchronization error dynamic, we design boundary controllers to achieve mean square asymptotical synchronization. By virtue of Lyapunov functional method and Wirtinger’s inequality, sufficient conditions are obtained for ensuring mean square asymptotical synchronization. When coupled SRDSs are subject to external disturbance, mean square H_∞ synchronization is investigated and corresponding criterion is presented under a designed boundary controller. In addition to focusing on systems with Neumann boundary conditions, we also briefly study coupled SRDSs with mixed boundary conditions and sufficient conditions are provided to achieve the desired performance. Numerical examples are used to verify the effectiveness of our theoretical results.

Original language	English
Pages (from-to)	1763-1773
Number of pages	11
Journal	Nonlinear Dynamics
Volume	94
Issue number	3
DOIs	https://doi.org/10.1007/s11071-018-4455-z
State	Published - 1 Nov 2018
Externally published	Yes

Keywords

Boundary control
H synchronization
Stochastic reaction–diffusion systems
Synchronization

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10.1007/s11071-018-4455-z

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title = "Synchronization of stochastic reaction–diffusion systems via boundary control",

abstract = "This paper studies the problem of mean square asymptotical synchronization and H∞ synchronization for coupled stochastic reaction–diffusion systems (SRDSs) via boundary control. Based on the deduced synchronization error dynamic, we design boundary controllers to achieve mean square asymptotical synchronization. By virtue of Lyapunov functional method and Wirtinger{\textquoteright}s inequality, sufficient conditions are obtained for ensuring mean square asymptotical synchronization. When coupled SRDSs are subject to external disturbance, mean square H∞ synchronization is investigated and corresponding criterion is presented under a designed boundary controller. In addition to focusing on systems with Neumann boundary conditions, we also briefly study coupled SRDSs with mixed boundary conditions and sufficient conditions are provided to achieve the desired performance. Numerical examples are used to verify the effectiveness of our theoretical results.",

keywords = "Boundary control, H synchronization, Stochastic reaction–diffusion systems, Synchronization",

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doi = "10.1007/s11071-018-4455-z",

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T1 - Synchronization of stochastic reaction–diffusion systems via boundary control

AU - Wu, Kai Ning

AU - Wang, Jian

AU - Lim, Cheng Chew

PY - 2018/11/1

Y1 - 2018/11/1

N2 - This paper studies the problem of mean square asymptotical synchronization and H∞ synchronization for coupled stochastic reaction–diffusion systems (SRDSs) via boundary control. Based on the deduced synchronization error dynamic, we design boundary controllers to achieve mean square asymptotical synchronization. By virtue of Lyapunov functional method and Wirtinger’s inequality, sufficient conditions are obtained for ensuring mean square asymptotical synchronization. When coupled SRDSs are subject to external disturbance, mean square H∞ synchronization is investigated and corresponding criterion is presented under a designed boundary controller. In addition to focusing on systems with Neumann boundary conditions, we also briefly study coupled SRDSs with mixed boundary conditions and sufficient conditions are provided to achieve the desired performance. Numerical examples are used to verify the effectiveness of our theoretical results.

AB - This paper studies the problem of mean square asymptotical synchronization and H∞ synchronization for coupled stochastic reaction–diffusion systems (SRDSs) via boundary control. Based on the deduced synchronization error dynamic, we design boundary controllers to achieve mean square asymptotical synchronization. By virtue of Lyapunov functional method and Wirtinger’s inequality, sufficient conditions are obtained for ensuring mean square asymptotical synchronization. When coupled SRDSs are subject to external disturbance, mean square H∞ synchronization is investigated and corresponding criterion is presented under a designed boundary controller. In addition to focusing on systems with Neumann boundary conditions, we also briefly study coupled SRDSs with mixed boundary conditions and sufficient conditions are provided to achieve the desired performance. Numerical examples are used to verify the effectiveness of our theoretical results.

KW - Boundary control

KW - H synchronization

KW - Stochastic reaction–diffusion systems

KW - Synchronization

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DO - 10.1007/s11071-018-4455-z

M3 - 文章

AN - SCOPUS:85049169554

SN - 0924-090X

VL - 94

SP - 1763

EP - 1773

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

IS - 3

ER -

Synchronization of stochastic reaction–diffusion systems via boundary control

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Keywords

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